Mirela_Buru There is actually no UserVoice site available that is suitable for me to place my request. I realize Exchange 2010 is going/gone away and so will/are Federation Trusts. Recreating the Federation Trust can be disruptive to users and (when there are many Accepted Domains) becomes a lot of work (i.e. creating public DNS proof records). A process to remove the expired certificate from the existing, otherwise fine trust, would be the customer-first approach.
If you look at Set-AuthConfig, you can see that there is an included parameter -ClearPreviousCertificate. That is exactly what would have been nice to have included for Set-FederationTrust. I realize it's too late to ask for Set-FederationTrust to be updated, especially in Exchange versions older than Exchange 2019. In place of that, some kind of similar blog post to this one, sharing a well-working solution, would be sufficient.
I hope you can agree that this blog post is at least loosely related to the topic I'm referring to. Every organization that has had a Federation Trust created more than 5 years ago faces this issue, with an expired certificate on every Exchange server, equaling one repetitive notification per server. It's messy and noisy, I'm not just making it up or being picky.