I run a spare server for emergencies? Do I need an additional certificate for this server?

If:

. you connect your spare server only in case of break-down of your main server.
· your spare serve has the same QDHN or IP address as the original one

Then:

You can install the same certificate as the one on your main server.

You cannot, however, have both servers on-line (i.e. exposed to the internet) simultaneously.