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

    <schemaVersion>X0304</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2011-08-19</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001491925</issuerCik>
        <issuerName>New Mountain Finance Holdings, L.L.C.</issuerName>
        <issuerTradingSymbol>NONE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001018327</rptOwnerCik>
            <rptOwnerName>KLINSKY STEVEN B</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O NEW MOUNTAIN CAPITAL, L.L.C.</rptOwnerStreet1>
            <rptOwnerStreet2>787 7TH AVENUE, 49TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Membership Units</value>
            </securityTitle>
            <transactionDate>
                <value>2011-08-19</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>13</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>11.99</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1807425</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Note</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Membership Units</value>
            </securityTitle>
            <transactionDate>
                <value>2011-08-22</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>6987</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>11.82</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1814412</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Note</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Membership Units</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>68965</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Note</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Membership Units</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>65792</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Note</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Membership Units</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>20221938</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Note</value>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The price reported is the weighted average price. New Mountain Finance Corporation directly owns Common Membership Units of New Mountain Finance Holdings, L.L.C. (the &quot;Units&quot;). Shares of New Mountain Finance Corporation were purchased in multiple transactions at prices ranging from $11.53 to $11.92, inclusive. The reporting person undertakes to provide to the SEC, the issuer and any security holder, upon request, full information regarding the number of shares and the prices at which the shares were purchased.</footnote>
        <footnote id="F2">The reporting person directly owns 1,814,412 shares of common stock of New Mountain Finance Corporation.  The reporting person may be deemed to beneficially own 1,814,412 of the Units owned by New Mountain Finance Corporation.  The reporting person disclaims beneficial ownership of these Units, except to the extent of his pecuniary interest therein.</footnote>
        <footnote id="F3">The Steven B. Klinsky Trust directly owns 68,965 shares of common stock of New Mountain Finance Corporation.  The reporting person may be deemed to beneficially own 68,965 of the Units owned by New Mountain Finance Corporation.  The reporting person disclaims beneficial ownership of these shares except to the extent of his pecuniary interest therein.</footnote>
        <footnote id="F4">New Mountain Guardian GP, L.L.C. directly owns 65,792 shares of common stock of New Mountain Finance Corporation. The reporting person is the sole owner of New Mountain Guardian GP, L.L.C. and, as a result, may be deemed to beneficially own 65,792 Units owned by New Mountain Finance Corporation. The reporting person disclaims beneficial ownership of these Units except to the extent of his pecuniary interest therein.</footnote>
        <footnote id="F5">New Mountain Finance AIV Holdings Corporation (&quot;AIV Holdings&quot;) and New Mountain Guardian AIV, L.P. (&quot;Guardian AIV&quot;) (indirectly through its wholly-owned subsidiary, AIV Holdings) own 20,221,938 Units.  New Mountain Investments III, L.L.C. is the general partner of Guardian AIV.  The reporting person is the managing member of New Mountain Investments III, L.L.C. and may be deemed to beneficially own these Units.  The reporting person disclaims beneficial ownership of these Units except to the extent of his pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Steven B. Klinsky</signatureName>
        <signatureDate>2011-08-24</signatureDate>
    </ownerSignature>
</ownershipDocument>
