This is a question I've been asked a number of times.
Usually, you just ping the metadata endpoint or the IDPInitiatedSignOn endpoint.
Then I found: AD FS Diagnostics Module.
"The AD FS Diagnostics Module contains commandlets to gather configuration information of an AD FS server, as well as commandlets to perform health checks to detect configuration issues based on common root causes identified during support engagements such as duplicate SPN, cert".
There are some other useful links on the LHS.
On my list to try out :-)