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| <?xml version="1.0" encoding="windows-1252"?> |
| <ownershipDocument> |
| <schemaVersion> X0306 </schemaVersion> |
| <documentType> 4 </documentType> |
| <periodOfReport> 2020-05-22 </periodOfReport> |
| <notSubjectToSection16> 0 </notSubjectToSection16> |
| <issuer> |
| | <issuerCik> 0000804753 </issuerCik> |
| | <issuerName> CERNER Corp </issuerName> |
| | <issuerTradingSymbol> CERN </issuerTradingSymbol> |
| | </issuer> |
| <reportingOwner> |
| | <reportingOwnerId> |
| | | <rptOwnerCik> 0001085324 </rptOwnerCik> |
| | | <rptOwnerName> ZOLLARS WILLIAM D </rptOwnerName> |
| | | </reportingOwnerId> |
| | <reportingOwnerAddress> |
| | | <rptOwnerStreet1> 2800 ROCKCREEK PARKWAY </rptOwnerStreet1> |
| | | <rptOwnerStreet2></rptOwnerStreet2> |
| | | <rptOwnerCity> NORTH KANSAS CITY </rptOwnerCity> |
| | | <rptOwnerState> MO </rptOwnerState> |
| | | <rptOwnerZipCode> 64117 </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 </value> |
| </securityTitle> |
| | | <transactionDate> |
| <value> 2020-05-22 </value> |
| </transactionDate> |
| | | <deemedExecutionDate></deemedExecutionDate> |
| | | <transactionCoding> |
| <transactionFormType> 4 </transactionFormType> |
| <transactionCode> A </transactionCode> |
| <equitySwapInvolved> 0 </equitySwapInvolved> |
| </transactionCoding> |
| | | <transactionTimeliness> |
| <value></value> |
| </transactionTimeliness> |
| | | <transactionAmounts> |
| <transactionShares> |
| <value> 3716 </value> |
| <footnoteId id="F1"/> |
| </transactionShares> |
| <transactionPricePerShare> |
| <value> 0.00 </value> |
| </transactionPricePerShare> |
| <transactionAcquiredDisposedCode> |
| <value> A </value> |
| </transactionAcquiredDisposedCode> |
| </transactionAmounts> |
| | | <postTransactionAmounts> |
| <sharesOwnedFollowingTransaction> |
| <value> 7272 </value> |
| <footnoteId id="F2"/> |
| </sharesOwnedFollowingTransaction> |
| </postTransactionAmounts> |
| | | <ownershipNature> |
| <directOrIndirectOwnership> |
| <value> D </value> |
| </directOrIndirectOwnership> |
| </ownershipNature> |
| | | </nonDerivativeTransaction> |
| | <nonDerivativeHolding> |
| | | <securityTitle> |
| <value> Common Stock </value> |
| </securityTitle> |
| | | <postTransactionAmounts> |
| <sharesOwnedFollowingTransaction> |
| <value> 25572 </value> |
| </sharesOwnedFollowingTransaction> |
| </postTransactionAmounts> |
| | | <ownershipNature> |
| <directOrIndirectOwnership> |
| <value> I </value> |
| </directOrIndirectOwnership> |
| <natureOfOwnership> |
| <value> by Revocable Trust </value> |
| </natureOfOwnership> |
| </ownershipNature> |
| | | </nonDerivativeHolding> |
| | </nonDerivativeTable> |
| <footnotes> |
| | <footnote id="F1"> These shares represent an award of restricted common stock that will vest on the earlier of May 18, 2021 or the calendar day immediately preceding the date of the Cerner Corporation 2021 annual meeting of shareholders. </footnote> |
| | <footnote id="F2"> Includes 3,716 shares of restricted common stock. </footnote> |
| | </footnotes> |
| <remarks></remarks> |
| <ownerSignature> |
| | <signatureName> /s/ Shane M. Dawson, by Power of Attorney </signatureName> |
| | <signatureDate> 2020-05-27 </signatureDate> |
| | </ownerSignature> |
| </ownershipDocument> |
