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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2007-08-29</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001352713</issuerCik>
        <issuerName>RAM Holdings Ltd.</issuerName>
        <issuerTradingSymbol>RAMR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001362766</rptOwnerCik>
            <rptOwnerName>Voldstad Conrad P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>RAM RE, RAM RE HOUSE</rptOwnerStreet1>
            <rptOwnerStreet2>46 REID STREET</rptOwnerStreet2>
            <rptOwnerCity>HAMILTON</rptOwnerCity>
            <rptOwnerState>D0</rptOwnerState>
            <rptOwnerZipCode>HM 12</rptOwnerZipCode>
            <rptOwnerStateDescription>BERMUDA</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares, par value $0.10 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2007-08-29</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>79400</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Of the 10,000 shares purchased, 100 shares were purchased at  $8.88, 100 shares were purchased at  $8.90,  100 shares were
 purchased at $8.92, 100  shares were purchased at $8.93, 1100 shares were purchased at $8.94, 2000 shares were purchased at
 $8.95, 300 shares were purchased at $8.96, 500 shares were purchased at $8.97,  700 shares were purchased at $8.98, 100
 shares were purchased at $8.99, 4200 shares were purchased at  $9.00, 400 shares were purchased at $9.01, 200 shares were
 purchased at $9.02 and 100 shares were purchased at $9.04.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Conrad P. Voldstad</signatureName>
        <signatureDate>2007-08-31</signatureDate>
    </ownerSignature>
</ownershipDocument>
