<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2013-05-14</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000927355</issuerCik>
        <issuerName>TESSCO TECHNOLOGIES INC</issuerName>
        <issuerTradingSymbol>TESS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001229699</rptOwnerCik>
            <rptOwnerName>SHAUGHNESSY DENNIS J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>777 SOUTH FLAGLER DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2>PHILLIPS POINT WEST TOWER SUITE 1500</rptOwnerStreet2>
            <rptOwnerCity>WEST PALM BEACH</rptOwnerCity>
            <rptOwnerState>FL</rptOwnerState>
            <rptOwnerZipCode>33401</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2013-05-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2811</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>59505</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2013-05-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>938</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>60443</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2013-05-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>61943</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2013-05-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>838</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>62781</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance Share Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F5"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2013-05-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2811</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2811</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>9724</value>
                    <footnoteId id="F6"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance Share Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F5"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2013-05-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>938</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>938</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8786</value>
                    <footnoteId id="F7"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Share Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F5"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2013-05-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7286</value>
                    <footnoteId id="F8"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Share Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F5"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2013-05-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>838</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F4"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>838</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>6448</value>
                    <footnoteId id="F9"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Share Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F5"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2013-05-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F10"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F10"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F10"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>9448</value>
                    <footnoteId id="F10"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">A Performance Share Unit, sometimes referred to as a Performance Stock Unit or PSU, represents the conditional right to receive one share of Common Stock. PSUs granted in April 2009 resulted in the earning, with respect to the fiscal year ended March 2010 and based on the extent to which certain performance criteria were satisfied during fiscal year 2010, of the right to receive 11,250 shares of Common Stock. Once earned, the PSUs vest and are paid through the issuance of shares of Common Stock in four approximately equal annual installments commencing on or about May 1, 2010, 2011, 2012 and 2013, subject to the reporting person's continued employment or association with the Issuer on the date such shares of Common Stock are to be issued.</footnote>
        <footnote id="F2">A Performance Share Unit, sometimes referred to as a Performance Stock Unit or PSU, represents the conditional right to receive one share of Common Stock. PSUs granted in April 2010 resulted in the earning, with respect to the fiscal year ended March 2011 and based on the extent to which certain performance criteria were satisfied during fiscal year 2011, of the right to receive 3,750 shares of Common Stock. Once earned, the PSUs vest and are paid through the issuance of shares of Common Stock in four approximately equal annual installments commencing on or about May 1, 2011, 2012, 2013 and 2014, subject to the reporting person's continued employment or association with the Issuer on the date such shares of Common Stock are to be issued.</footnote>
        <footnote id="F3">A Restricted Share Unit, sometimes referred to as a Restricted Stock Unit or RSU, represents the conditional right to receive one share of Common Stock. RSUs granted in April 2011 resulted in the right to receive 6,000 shares of Common Stock. The RSUs vest and are paid through the issuance of shares of Common Stock in four approximately equal annual installments commencing on or about May 1, 2012, 2013, 2014 and 2015, subject to the reporting person's continued employment or association with the Issuer on the date such shares of Common Stock are to be issued.</footnote>
        <footnote id="F4">A Restricted Share Unit, sometimes referred to as a Restricted Stock Unit or RSU, represents the conditional right to receive one share of Common Stock. RSUs granted in April 2012 resulted in the right to receive 3,350 shares of Common Stock. The RSUs vest and are paid through the issuance of shares of Common Stock in four approximately equal annual installments commencing on or about May 1, 2013, 2014, 2015 and 2016, subject to the reporting person's continued employment or association with the Issuer on the date such shares of Common Stock are to be issued.</footnote>
        <footnote id="F5">1 for 1</footnote>
        <footnote id="F6">In respect of the PSUs granted in April 2009 with respect to fiscal year 2010, on April 27, 2010, the reporting person earned the right to receive 11,250 shares of Common Stock. The reporting person was associated with the Issuer on April 27, 2010, resulting in the vesting and issuance of 2,813 of the 11,250 shares of Common Stock so earned. On April 26, 2011, the reporting person continued to be associated with the Issuer, resulting in the vesting and issuance of another 2,813 shares of Common Stock so earned. On May 3, 2012, the reporting person continued to be associated with the Issuer, resulting in the vesting and issuance of another 2,813 shares of Common Stock so earned. On May 14, 2013, the reporting person continued to be associated with the Issuer, resulting in the vesting and issuance of the remaining 2,811 shares of Common Stock so earned.</footnote>
        <footnote id="F7">In respect of the PSUs granted in April 2010 with respect to fiscal year 2011, on April 26, 2011, the reporting person earned the right to receive 3,750 shares of Common Stock. The reporting person was associated with the Issuer on April 26, 2011, resulting in the vesting and issuance of 938 of the 3,750 shares of Common Stock so earned. On May 3, 2012, the reporting person continued to be associated with the Issuer, resulting in the vesting and issuance of another 938 shares of Common Stock so earned. On May 14, 2013, the reporting person continued to be associated with the Issuer, resulting in the vesting and issuance of another 938 shares of Common Stock so earned. The remaining 936 shares have been earned, but are not yet vested.</footnote>
        <footnote id="F8">A Restricted Share Unit, sometimes referred to as a Restricted Stock Unit or RSU, represents the conditional right to receive one share of Common Stock. RSUs are subject to time vesting but not performance vesting. These RSUs will vest and the underlying shares of Common Stock will be issued in equal annual installments of 1,500 shares commencing on or about May 1, 2012, 2013, 2014 and 2015, generally subject to the reporting person's continued association with the Issuer on the date such shares of Common Stock are to be issued. The reporting person was associated with the Issuer on May 3, 2012, resulting in the vesting and issuance of 1,500 of the 6,000 shares of Common Stock covered by the RSU. On May 14, 2013, the reporting person continued to be associated with the Issuer, resulting in the vesting and issuance of another 1,500 shares of Common Stock covered by the RSU. The remaining 3,000 remain subject to issuance upon future vesting.</footnote>
        <footnote id="F9">A Restricted Share Unit, sometimes referred to as a Restricted Stock Unit or RSU, represents the conditional right to receive one share of Common Stock. RSUs are subject to time vesting but not performance vesting. These RSUs will vest and the underlying shares of Common Stock will be issued in equal annual installments of approximately 838 shares commencing on or about May 1, 2013, 2014, 2015 and 2016, generally subject to the reporting person's continued association with the Issuer on the date such shares of Common Stock are to be issued. The reporting person was associated with the Issuer on May 14, 2013, resulting in the vesting and issuance of 838 of the 3,350 shares of Common Stock covered by the RSU. The remaining 2,512 remain subject to issuance upon future vesting.</footnote>
        <footnote id="F10">A Restricted Share Unit, sometimes referred to as a Restricted Stock Unit or RSU, represents the conditional right to receive one share of Common Stock. RSUs are subject to time vesting but not performance vesting. These RSUs will vest and the underlying shares of Common Stock will be issued in equal annual installments of approximately 750 shares commencing on or about May 1, 2014, 2015, 2016 and 2017, generally subject to the reporting person's continued association with the Issuer on the date such shares of Common Stock are to be issued. Accordingly, as of May 14, 2013, 3,000 RSU's have been granted, but are not yet vested.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Dennis J. Shaughnessy by Aric Spitulnik by Power of Attorney</signatureName>
        <signatureDate>2013-05-16</signatureDate>
    </ownerSignature>
</ownershipDocument>
