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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2007-06-29</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001179755</issuerCik>
        <issuerName>ENDURANCE SPECIALTY HOLDINGS LTD</issuerName>
        <issuerTradingSymbol>ENH</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001198607</rptOwnerCik>
            <rptOwnerName>DELCOL JOHN V</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O ENDURANCE SPECIALTY HOLDINGS LTD.</rptOwnerStreet1>
            <rptOwnerStreet2>WELLESLEY HOUSE, 90 PITTS BAY ROAD</rptOwnerStreet2>
            <rptOwnerCity>PEMBROKE</rptOwnerCity>
            <rptOwnerState>D0</rptOwnerState>
            <rptOwnerZipCode>HM 08</rptOwnerZipCode>
            <rptOwnerStateDescription>BERMUDA</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>General Counsel and Secretary</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares, par value $1.00 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2007-09-28</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
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                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
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                    <value>72694</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
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            </securityTitle>
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            </conversionOrExercisePrice>
            <transactionDate>
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            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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            <transactionTimeliness>
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            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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            <expirationDate>
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            </expirationDate>
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                </underlyingSecurityTitle>
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                </underlyingSecurityShares>
            </underlyingSecurity>
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                </transactionShares>
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            </underlyingSecurity>
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                </underlyingSecurityShares>
            </underlyingSecurity>
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                </sharesOwnedFollowingTransaction>
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                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
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            </transactionDate>
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            <transactionTimeliness>
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                </transactionShares>
                <transactionPricePerShare>
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                </underlyingSecurityShares>
            </underlyingSecurity>
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        <derivativeTransaction>
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            </securityTitle>
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            <transactionDate>
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                <transactionPricePerShare>
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                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2009-03-01</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Ordinary Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>6449</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On September 28, 2007, pursuant to the terms of the Issuer's restricted share unit exchange program, the Issuer cancelled restricted share units previously granted to the Reporting Person.  In exchange for the restricted share units, the Reporting Person received an equivalent number of restricted shares.</footnote>
        <footnote id="F2">The dividend restricted share units granted were cancelled on September 28, 2007 in accordance with the terms of the Restricted Share Agreement between the Issuer and the Reporting Person.  In exchange, the Reporting Person received an equivalent number of restricted shares as reported in Table I above.</footnote>
        <footnote id="F3">The number of dividend restricted share units issued was determined pursuant to the terms of the agreement governing the securities based on (i) the closing sale price for the Company's ordinary shares on June 29, 2007 of $39.82 and (ii) the issuance by the Company of a $0.25 per share dividend on that date.</footnote>
        <footnote id="F4">The restricted share units are forfeitable only upon violation of a non-competition restriction and are converted into ordinary shares or their cash equivalent on March 1, 2008.</footnote>
        <footnote id="F5">The number of restricted share units issued was determined pursuant to the terms of the agreement governing the securities based on (i) the cumulative dividends that would otherwise have been used to reduce the strike price on options previously granted to the holder in order to make such options  compliant with Section 409A of the Internal Revenue Code and the regulations promulgated by the U.S. Internal Revenue Service under Section 409A and (ii) the closing sale price of the Company's ordinary shares on the dates the dividends were originally paid.</footnote>
        <footnote id="F6">The restricted share units are forfeitable only upon violation of a non-competition restriction and are converted into ordinary shares or their cash equivalent on March 1, 2009.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ John V. Del Col</signatureName>
        <signatureDate>2007-10-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
