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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-12-23</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001588869</issuerCik>
        <issuerName>Cambridge Capital Acquisition Corp</issuerName>
        <issuerTradingSymbol>CAMB</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001087395</rptOwnerCik>
            <rptOwnerName>GANTCHER NATHAN</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CAMBRIDGE CAPITAL ACQUISITION CORP</rptOwnerStreet1>
            <rptOwnerStreet2>525 SOUTH FLAGLER DRIVE, SUITE 201</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>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-12-23</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>20644</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>83702</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Gantcher Family Limited Partnership</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-12-23</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>83702</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Gantcher Family Limited Partnership</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Warrants</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>11.50</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-12-23</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>44346</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2015-12-23</value>
            </exerciseDate>
            <expirationDate>
                <value>2018-12-23</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>44346</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Gantcher Family Limited Partnership</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">These securities were transferred to third parties as consideration for such third parties purchasing shares of common stock of the issuer and agreeing not to seek conversion of such shares in connection with the issuer's business combination with Ability Computer &amp; Software Industries Ltd.</footnote>
        <footnote id="F2">Gantcher Family Partners LLC is the general partner of Gantcher Family Limited Partnership.  The Reporting Person is the managing member of Gantcher Family Partners LLC.</footnote>
        <footnote id="F3">On September 6, 2015, Cambridge Capital Acquisition Corporation (the &quot;Issuer&quot;), Cambridge Holdco Corp. (&quot;Holdco&quot;), Ability Computer &amp; Software Industries Ltd. (&quot;Ability&quot;) and the shareholders of Ability entered into an Agreement and Plan of Reorganization (the &quot;Merger Agreement&quot;), pursuant to which, and subject to the terms and conditions thereof, on December 23, 2015 (the &quot;Closing Date&quot;) the Issuer merged with and into Holdco, with Holdco surviving the merger. On the Closing Date, pursuant to the Merger Agreement, and subject to the terms and conditions thereof, at the effective time of the merger, Mr. Gantcher disposed of 83,702 shares of common stock of the Issuer in exchange for the same number of shares in Holdco.</footnote>
        <footnote id="F4">On the Closing Date, pursuant to the Merger Agreement, and subject to the terms and conditions thereof, at the effective time of the merger, the Warrants were assumed by Holdco in the Merger.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Nathan Gantcher</signatureName>
        <signatureDate>2016-01-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
