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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-11-20</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001822479</issuerCik>
        <issuerName>Sotera Health Co</issuerName>
        <issuerTradingSymbol>SHC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001309092</rptOwnerCik>
            <rptOwnerName>Donnini David</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>300 N. LASALLE STREET, SUITE 5600</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60654</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $0.01 par value per share (&quot;Common Stock&quot;)</value>
            </securityTitle>
            <transactionDate>
                <value>2020-11-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5869</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5869</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">These securities consist of 5,869 Restricted Stock Units (&quot;RSUs&quot;) that were granted on November 20, 2020, pursuant to the terms of an RSU agreement under the Sotera Health Company 2020 Omnibus Incentive Plan. Each RSU represents the Reporting Person's right to receive one share of Common Stock, subject to vesting conditions. The RSUs will vest in full on the date immediately prior to the Issuer's next regular annual shareholders meeting, subject to the Reporting Person's continued service as a non-employee director of the Issuer through such date.</footnote>
    </footnotes>

    <remarks>The Power of Attorney for Mr. Donnini is filed as an exhibit to the Form 3 filed by Mr. Donnini with the Securities and Exchange Commission on November 20, 2020, which is hereby incorporated by reference.</remarks>

    <ownerSignature>
        <signatureName>/s/ Jessica L.M.H. Epp, as attorney in fact for David Donnini</signatureName>
        <signatureDate>2020-11-24</signatureDate>
    </ownerSignature>
</ownershipDocument>
