<?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>0000941885</rptOwnerCik>
            <rptOwnerName>BARNHILL ROBERT B JR</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>11126 MCCORMICK ROAD</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>HUNT VALLEY</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>21031</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>CEO, President</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>6500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1825636</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F9"/>
                </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>2810</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1828446</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F9"/>
                </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>1889</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1830335</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F9"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-05-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3354</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1826981</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F9"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance 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>6500</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>6500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>11284</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>2015-05-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2810</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>2810</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8474</value>
                    <footnoteId id="F7"/>
                </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>2015-05-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1889</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>1889</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>6585</value>
                    <footnoteId id="F8"/>
                </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 2011 resulted in the earning, with respect to the fiscal year ended March 2012 and based on the extent to which certain performance criteria were satisfied during fiscal year 2012, of the right to receive 26,000 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, 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 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 2012 resulted in the earning, with respect to the fiscal year ended March 2013 and based on the extent to which certain performance criteria were satisfied during fiscal year 2013, of the right to receive 11,240 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, 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 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 2013 resulted in the earning, with respect to the fiscal year ended March 2014 and based on the extent to which certain performance criteria were satisfied during fiscal year 2014, of the right to receive 7,555 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, 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">$24.15 -- closing market price on May 11, 2015.</footnote>
        <footnote id="F5">1 for 1</footnote>
        <footnote id="F6">In respect of the PSUs granted in April 2011 with respect to fiscal year 2012, on May 3, 2012, the reporting person earned the right to receive 26,000 shares of Common Stock. The reporting person was associated with the Issuer on May 3, 2012, resulting in the vesting and issuance of 6,500 of the 26,000 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 6,500 shares of Common Stock so earned. On May 8, 2014, the reporting person continued to be associated with the Issuer, resulting in the vesting and issuance of another 6,500 shares of Common Stock so earned. On May 11, 2015, the reporting person continued to be associated with the Issuer, resulting in the vesting and issuance of the remaining 6,500 shares of Common Stock so earned.</footnote>
        <footnote id="F7">In respect of the PSUs granted in April 2012 with respect to fiscal year 2013, on May 14, 2013, the reporting person earned the right to receive 11,240 shares of Common Stock. The reporting person was associated with the Issuer on May 14, 2013, resulting in the vesting and issuance of 2,810 of the 11,240 shares of Common Stock so earned. On May 8, 2014, the reporting person continued to be associated with the Issuer, resulting in the vesting and issuance of another 2,810 shares of Common Stock so earned. On May 11, 2015, the reporting person continued to be associated with the Issuer, resulting in the vesting and issuance of another 2,810 shares of Common Stock so earned. The remaining 2,810 shares have been earned, but are not yet vested.</footnote>
        <footnote id="F8">In respect of the PSUs granted in April 2013 with respect to fiscal year 2014, on May 8, 2014, the reporting person earned the right to receive 7,555 shares of Common Stock. The reporting person was associated with the Issuer on May 8, 2014, resulting in the vesting and issuance of 1,889 of the 7,555 shares of Common Stock so earned. On May 11, 2015, the reporting person continued to be associated with the Issuer, resulting in the vesting and issuance of another 1,889 shares of Common Stock so earned. The remaining 3,777 shares have been earned, but are not yet vested.</footnote>
        <footnote id="F9">All shares are owned directly, except for the following shares, which are owned indirectly: 2,676 shares which are owned through 401(k) plan, 325,500 that are owned by the reporting person's spouse and children and 21,500 shares held by a charitable trust.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Robert B. Barnhill, Jr. by Aric Spitulnik by Power of Attorney</signatureName>
        <signatureDate>2015-05-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
