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

    <schemaVersion>X0407</schemaVersion>

    <documentType>4</documentType>

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

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001484729</rptOwnerCik>
            <rptOwnerName>Leheny A. Rachel</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CALCIMEDICA, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>505 COAST S. BLVD. #202</rptOwnerStreet2>
            <rptOwnerCity>LA JOLLA</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92037</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Executive Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

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            </postTransactionAmounts>
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                </directOrIndirectOwnership>
                <natureOfOwnership>
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                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F18"/>
            </exerciseDate>
            <expirationDate>
                <value>2023-03-19</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>12342</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12342</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Warrant</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>27.94</value>
            </conversionOrExercisePrice>
            <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>
                <transactionShares>
                    <value>9935</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F22"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F13"/>
            </exerciseDate>
            <expirationDate>
                <value>2026-02-22</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>9935</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>9935</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Valence Investments SPV V, LLC</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Warrant</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>27.94</value>
            </conversionOrExercisePrice>
            <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>
                <transactionShares>
                    <value>9935</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F22"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F13"/>
            </exerciseDate>
            <expirationDate>
                <value>2026-05-25</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>9935</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>9935</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Valence Investments SPV V, LLC</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Received in exchange for an aggregate of 12,395,423 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">The Reporting Person, a co-founder and managing director of Valence Investments SPV IV, LLC (&quot;Valence IV&quot;), Valence Investments SPV V, LLC (&quot;Valence V&quot;) and Valence Investments SPV VI, LLC (Valence VI), may be deemed to beneficially own the securities held by Valence IV, Valence V and Valence VI (the &quot;Valence Securities&quot;).  The Reporting Person disclaims beneficial ownership of the Valence Securities except to the extent of her pecuniary interest therein.</footnote>
        <footnote id="F3">Received in exchange for 2,299,564 shares of the common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F4">Received in exchange for 10,975,977 shares of the common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F5">25% of the shares subject to the option vested on April 30, 2020 and the balance of the shares vest in a series of thirty-six (36) successive equal monthly installments thereafter.</footnote>
        <footnote id="F6">Received in exchange for a stock option to acquire 390,000 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F7">Received in exchange for a stock option to acquire 2,644,900 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F8">25% of the shares subject to the option vested on June 30, 2020 and the balance of the shares vest in a series of thirty-six (36) successive equal monthly installments thereafter.</footnote>
        <footnote id="F9">Upon the closing of the Merger, each outstanding option to purchase shares of CalciMedica common stock was assumed by the Issuer and converted into an option to purchase the Issuer's common stock.</footnote>
        <footnote id="F10">Received in exchange for a stock option to acquire 1,054,921 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F11">Beginning on February 22, 2021, the shares subject to the option vest in a series of forty-eight (48) successive equal monthly installments.</footnote>
        <footnote id="F12">Received in exchange for a stock option to acquire 484,863 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F13">Immediately exercisable.</footnote>
        <footnote id="F14">Received in exchange for a stock option to acquire 688,404 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F15">Received in exchange for a stock option to acquire 123,357 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F16">Received in exchange for a stock option to acquire 70,490 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F17">Received in exchange for a stock option to acquire 36,905 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F18">Beginning on November 22, 2022, the shares subject to the option vest in a series of forty-eight (48) successive equal monthly installments.</footnote>
        <footnote id="F19">Received in exchange for a stock option to acquire 59,641 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F20">Received in exchange for a stock option to acquire 1,057,071 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F21">Received in exchange for a stock option to acquire 428,566 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F22">Received in exchange for a stock option to acquire 344,934 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>By John Dunn, Attorney-in-Fact</signatureName>
        <signatureDate>2023-03-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
