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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-05-11</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>2015-05-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>18305</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-05-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>838</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>19143</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-05-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>750</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>19893</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-05-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>20393</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Share Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F5"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-05-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1500</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>1500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5924</value>
                    <footnoteId id="F6"/>
                    <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>2015-05-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>838</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>838</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5086</value>
                    <footnoteId id="F8"/>
                    <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>2015-05-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>750</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>750</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4336</value>
                    <footnoteId id="F10"/>
                </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>2015-05-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>500</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>500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3836</value>
                    <footnoteId id="F11"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">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="F2">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="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 2013 resulted in the right to receive 3,000 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, 2014, 2015, 2016 and 2017, 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 2014 resulted in the right to receive 2,000 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, 2015, 2016, 2017 and 2018, 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">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.</footnote>
        <footnote id="F7">[Footnote #6 continued] On May 8, 2014, 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. On May 11, 2015, the reporting person continued to be associated with the Issuer, resulting in the vesting and issuance of the remaining 1,500 shares of Common Stock covered by the RSU.</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 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. On May 8, 2014, the reporting person continued to be associated with the Issuer, resulting in the vesting and issuance of another 838 shares of Common Stock covered by the RSU.</footnote>
        <footnote id="F9">[Footnote #8 continued] On May 11, 2015, the reporting person continued to be associated with the Issuer, resulting in the vesting and issuance of another 838 shares of Common Stock covered by the RSU. The remaining 836 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 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. The reporting person was associated with the Issuer on May 8, 2014, resulting in the vesting and issuance of 750 of the 3,000 shares of Common Stock covered by the RSU. On May 11, 2015, the reporting person continued to be associated with the Issuer, resulting in the vesting and issuance of another 750 shares of Common Stock covered by the RSU. The remaining 1,500 remain subject to issuance upon future vesting.</footnote>
        <footnote id="F11">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 500 shares commencing on or about May 1, 2015, 2016, 2017 and 2018, 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 11, 2015, resulting in the vesting and issuance of 500 of the 2,000 shares of Common Stock covered by the RSU. The remaining 1,500 remain subject to issuance upon future vesting.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Dennis J. Shaughnessy by Aric Spitulnik by Power of Attorney</signatureName>
        <signatureDate>2015-05-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
