Some time back I got few tickets where users were complaining about free/busy not working between on perm exchange and office365, my issue was resolved after following below mentioned action plan, the issue was with delegation Trust and Token Validation, after I refresh Federation Trust metadata issue Stand Resolved.
In order to test this: Run the below command on On-Premise Exchange Powershell
Test-FederationTrust -UserIdentity Admin@letsexchange.in
Id : FederationMetadataType : Error Message : The federation trust doesn't contain the same certificates published by the security token service in its federation metadata.Id : TokenValidationType : Error Message : Failed to validate delegation token.
To fixed the Error I ran the below Command.
Get-FederationTrust | Set-FederationTrust –RefreshMetadata
This will refresh the Trust metadata and the free/busy issue will be resolved for you.
Re run the below command to cross check if the error are gone now
Test-FederationTrust -UserIdentity Admin@letsexchange.in
Hopefully errors will be gone like above picture and you should be good J