The certificate is not bound to the IP address, but to the domain name......unless the IP address is being used in the address bar to access the web server.

If your hosting provider bought the certificate for you:
If you are moving the certificate to another hosting provider you will need to ask your present hosting provider to backup the certificate and private key for you, as you will need to install these on the new hosting machine.
Details on backing up the certificate and private key can be found in our FAQs

If your just want to copy the certificate and private key to a backup server:
If the second server is going to be a backup server, then you can use export and import the same certificate to the second server.
Details on backing up the certificate and private key, and importing it to another machine, can be found in our FAQs