<?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>0001968792</rptOwnerCik>
            <rptOwnerName>Dunn Michael J.</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>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President and COO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <derivativeTable>
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                <value>Employee Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>1.39</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-03-20</value>
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            <deemedExecutionDate></deemedExecutionDate>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
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                </transactionShares>
                <transactionPricePerShare>
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            <expirationDate>
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            </expirationDate>
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            <underlyingSecurity>
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            <transactionTimeliness>
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            <expirationDate>
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            <underlyingSecurity>
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        <derivativeTransaction>
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            <deemedExecutionDate></deemedExecutionDate>
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            <transactionTimeliness>
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            <exerciseDate>
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            <expirationDate>
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            <underlyingSecurity>
                <underlyingSecurityTitle>
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        <derivativeTransaction>
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                    <value>D</value>
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        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>17.34</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-03-20</value>
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            <deemedExecutionDate></deemedExecutionDate>
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                <transactionCode>A</transactionCode>
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            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
                <transactionShares>
                    <value>24747</value>
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                <transactionPricePerShare>
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                    <footnoteId id="F15"/>
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                <transactionAcquiredDisposedCode>
                    <value>A</value>
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            <exerciseDate>
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            <expirationDate>
                <value>2033-03-19</value>
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                    <value>Common Stock</value>
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                    <value>D</value>
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        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (right to buy)</value>
            </securityTitle>
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                <value>17.34</value>
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            <transactionTimeliness>
                <value></value>
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                <transactionShares>
                    <value>847</value>
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                    <footnoteId id="F4"/>
                    <footnoteId id="F16"/>
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                    <value>A</value>
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                <value>2023-03-19</value>
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                <underlyingSecurityTitle>
                    <value>Common Stock</value>
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    </derivativeTable>

    <footnotes>
        <footnote id="F1">Immediately exercisable.</footnote>
        <footnote id="F2">Received in exchange for a stock option to acquire 408,402 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 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. Subsequent to the Merger, the name of the Issuer was changed from Graybug Vision, Inc. to CalciMedica, Inc.</footnote>
        <footnote id="F3">Received in exchange for a stock option to acquire 790,880 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F4">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="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 300,000 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F7">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="F8">Received in exchange for a stock option to acquire 819,064 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F9">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="F10">Received in exchange for a stock option to acquire 274,848 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F11">Received in exchange for a stock option to acquire 456,522 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F12">Received in exchange for a stock option to acquire 45,955 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F13">Received in exchange for a stock option to acquire 67,873 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F14">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="F15">Received in exchange for a stock option to acquire 859,280 shares of common stock of CalciMedica pursuant to the Merger Agreement.</footnote>
        <footnote id="F16">Received in exchange for a stock option to acquire 29,420 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>
