Hi Frank,
According to your description, I understand that the certificate used for ADFS expired, and you want to renew this certificate. If there are any misunderstanding, please feel free to post.
Based on my experience, the certificate will update to all the members of the federation server farm automatically, we don't need to update it manually. For this issue, I suggest you refer to the section Resolution 2: Renew the token-signing certificate via the following link:
http://support.microsoft.com/kb/2383983/en-us
If you have deployed ADFS with Office 365, we have a Federation Metadata Update Tool available, this update tool will automatically update the Office 365 service using Update-MsolFederatedDomain cmdlet when the ADFS token signing certificate renews on an annual basis. For more information about this tool, please visit here.
Moreover, since this issue is more related to how to refresh the certificate on ADFS server, I sincerely suggest you also post this question in ADFS forum, the engineer there may provide more professional suggestions for you, thank you for your understanding.
The ADFS forum URL:
http://social.msdn.microsoft.com/Forums/en-US/geneva/threads/
Thanks,
Jolin Qiao