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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2008-03-20</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, $0.10 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2008-03-20</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>46000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>151400</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Of the 46,000 shares purchased, 10,000 were purchased at $1.3999, 2,000 were purchased at $1.3999, 5,000 were purchased at
 $1.40, 1,000 were purchased at $1.40, 1,000 were purchased at $1.3492, 23,000 were purchased at $1.4627, and 4,000 were
 purchased at $1.4767.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Conrad P Voldstad</signatureName>
        <signatureDate>2008-03-24</signatureDate>
    </ownerSignature>
</ownershipDocument>
