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

    <schemaVersion>X0508</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2023-03-20</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001534133</issuerCik>
        <issuerName>CalciMedica, Inc.</issuerName>
        <issuerTradingSymbol>CALC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001306717</rptOwnerCik>
            <rptOwnerName>Sanderling Venture Partners VI LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1300 S. EL CAMINO REAL SUITE 203</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SAN MATEO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94402</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001306695</rptOwnerCik>
            <rptOwnerName>Sanderling Venture Partners VI Co Investment Fund LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1300 S EL CAMINO REAL</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 203</rptOwnerStreet2>
            <rptOwnerCity>SAN MATEO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94402</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001429588</rptOwnerCik>
            <rptOwnerName>Sanderling Ventures Management VI</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1300 S EL CAMINO REAL</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 203</rptOwnerStreet2>
            <rptOwnerCity>SAN MATEO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94402</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001429283</rptOwnerCik>
            <rptOwnerName>Sanderling VI Beteiligungs GmbH &amp; Co KG</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1300 S EL CAMINO REAL</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 203</rptOwnerStreet2>
            <rptOwnerCity>SAN MATEO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94402</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001429282</rptOwnerCik>
            <rptOwnerName>Sanderling VI Limited Partnership</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1300 S EL CAMINO REAL</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 203</rptOwnerStreet2>
            <rptOwnerCity>SAN MATEO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94402</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001565862</rptOwnerCik>
            <rptOwnerName>Sanderling Ventures VII, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1300 S. EL CAMINO REAL</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 203</rptOwnerStreet2>
            <rptOwnerCity>SAN MATEO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94402</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001678656</rptOwnerCik>
            <rptOwnerName>Sanderling Ventures VII Annex Fund, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1300 S EL CAMINO REAL</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 203</rptOwnerStreet2>
            <rptOwnerCity>SAN MATEO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94402</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001993457</rptOwnerCik>
            <rptOwnerName>Sanderling Ventures Management VII</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1300 S. EL CAMINO REAL SUITE 203</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SAN MATEO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94402</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001993660</rptOwnerCik>
            <rptOwnerName>Sanderling Ventures VII (Canada), L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1300 S. EL CAMINO REAL SUITE 203</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SAN MATEO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94402</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2023-03-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
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                </transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
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                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2023-03-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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            <transactionTimeliness>
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                </transactionAcquiredDisposedCode>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Sanderling Venture Partners VI Co-Investment Fund, L.P.</value>
                </natureOfOwnership>
            </ownershipNature>
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        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
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            <transactionTimeliness>
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                </sharesOwnedFollowingTransaction>
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                </natureOfOwnership>
            </ownershipNature>
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        <nonDerivativeTransaction>
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                <value>Common Stock</value>
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                    <value>7456</value>
                </transactionShares>
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                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Sanderling VI Beteligungs GmbH &amp; Co KG</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
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            </transactionDate>
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    <footnotes>
        <footnote id="F1">Received in exchange for 24,423,158 shares of common stock of CalciMedica, Inc. (&quot;CalciMedica&quot;) pursuant to an Agreement and Plan of Merger and Reorganization (the &quot;Merger Agreement&quot;) by and among CalciMedica, the Issuer and Camaro Merger Sub, Inc., a wholly-owned subsidiary of the Issuer (&quot;Merger Sub&quot;). Under the terms of the Merger Agreement, on March 20, 2023, Merger Sub merged with and into CalciMedica (the &quot;Merger&quot;), with CalciMedica surviving the Merger as a wholly-owned subsidiary of the Issuer. Upon the closing of the Merger, each share of CalciMedica common stock was converted into the right to receive 0.0288 of a share of the Issuer's common stock. Subsequent to the Merger, the name of the Issuer was changed from Graybug Vision, Inc. to CalciMedica, Inc.</footnote>
        <footnote id="F2">Received in exchange for 20,234,606 shares of the common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F3">Received in exchange for 613,943 shares of the common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F4">Received in exchange for 258,883 shares of the common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F5">Received in exchange for 308,455 shares of the common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F6">Received in exchange for 8,356,779 shares of the common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F7">Received in exchange for 500,854 shares of the common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F8">Received in exchange for 2,195,354 shares of the common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F9">The Reporting Person, a director of Sanderling Ventures, may be deemed to beneficially own the Sanderling VII Securities. The Reporting Person disclaims beneficial ownership of these securities except to the extent of his pecuniary interest therein.</footnote>
        <footnote id="F10">Received in exchange for 53,733 shares of the common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F11">Immediately exercisable.</footnote>
        <footnote id="F12">Received in exchange for a warrant to purchase 92,748 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F13">Received in exchange for a warrant to purchase 574,269 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F14">Received in exchange for a warrant to purchase 93,225 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F15">Received in exchange for a warrant to purchase 66,305 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F16">Received in exchange for a warrant to purchase 237,911 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F17">Received in exchange for a warrant to purchase 534,815 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F18">Received in exchange for a warrant to purchase 8,203 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F19">Received in exchange for a warrant to purchase 6,343 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F20">Received in exchange for a warrant to purchase 291,407 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F21">Received in exchange for a warrant to purchase 429,837 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F22">Received in exchange for a warrant to purchase 76,470 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F23">Received in exchange for a warrant to purchase 112,796 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F24">Received in exchange for a warrant to purchase 19,754 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F25">Received in exchange for a warrant to purchase 29,139 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F26">Received in exchange for a warrant to purchase 3,915 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F27">Received in exchange for a warrant to purchase 5,775 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Sanderling Venture Partners VI , L.P., By: /s/ Fred Middleton, Managing Director of Middleton, McNeil &amp; Mills Associates VI, L.P., its General Partner</signatureName>
        <signatureDate>2023-10-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Sanderling Venture Partners VI Co-Investment Fund, L.P., By: /s/ Fred Middleton, Managing Director of Middleton, McNeil &amp; Mills Associates VI, LLC, its General Partner</signatureName>
        <signatureDate>2023-10-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Sanderling Ventures Management VI, By: /s/ Fred Middleton, Owner</signatureName>
        <signatureDate>2023-10-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Sanderling VI Beteiligungs GmbH &amp; Co. KG, By: /s/ Fred Middleton, Managing Director of Middleton, McNeil &amp; Mills Associates VI, LLC, its Managing Limited Partner</signatureName>
        <signatureDate>2023-10-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Sanderling VI Limited Partnership, By: /s/ Fred Middleton, Managing Director of Middleton, McNeil &amp; Mills Associates VI, LLC, its Investment General Partner</signatureName>
        <signatureDate>2023-10-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Sanderling Ventures VII, L.P. , By: /s/ Fred Middleton, Managing Director of M4 Partners VII, LLC, its General Partner</signatureName>
        <signatureDate>2023-10-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Sanderling Ventures VII Annex Fund, L.P., By: /s/ Fred Middleton, Managing Director of M4 Partners VII Annex, LLC, its General Partner</signatureName>
        <signatureDate>2023-10-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Sanderling Ventures Management VII, By: /s/ Fred Middleton, Owner</signatureName>
        <signatureDate>2023-10-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Sanderling Ventures VII (Canada), L.P., By: /s/ D. Michael Dixon, President of Sanderling Ventures VII (Canada) GP Inc., General Partner of Sanderling Ventures VII (Canada) G.P., L.P, its General Partner</signatureName>
        <signatureDate>2023-10-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
