SSL certificates are tied to a single IP address in so far as that you can only have one certificate bound to a given IP address. The certificates themselves are expected to match the Common Name (CN) which is typically the hostname entered into DNS and configured for the service (IMAP, HTTPS, SMTP, etc).
That said the moving of servers and changing the IP address is not a problem so long as you take the necessary steps to update the DNS for the respective hostname entry to point to the new IP address. As mentioned you can limit the potential time by lowering the TTL so that the change propagates quickly, you can also make the DNS IP address change before actually moving the server so the update will go into affect before the change and thus lowering the possible unreachability.