I recently was asked to help troubleshoot an issue where the client was unable to add the ADFS proxy server despite the fact that they can successfully contact the service.
Unable to establish a trust between the federation server proxy and the Federation Service. Ensure that the provided credentials are valid credentials for establishing a trust or ensure that the Federation Service address is correct, and then try again
Going through the normal process of adding an ADFS proxy, the Test Connection was successful
Contact the Federation Service was successful
But you get a credential prompt
Then the error appears
Eventlog event that is logged from the error.
After troubleshooting this error I came to realize that the certificate that was used was not correct. The client had a multi-name certificate and the SPN on the certificate did not match the ADFS Farm name.
Resolution was to get a new public certificate with a single name and match the SPN to the ADFS Farm Name
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Office 365 MVP