Migrate SSL to new server without downtime on old server

I have an SSL certificate for a Glassfish server running on Debian in production. I am planning on replacing that server with a new Glassfish server running Oracle Linux. Since my SSL certificate is expiring in the next few months, this is what I wanted to do. The server URL will remain the same on the new server.

I would like to setup the new server and get it all configured. I’d like to issue a new SSL certificate for this new server and test it before shutting down the old server. If I issue a new SSL certificate for the new server, will it invalidate the existing SSL certificate on the old server?

I was told that I can get the SSL certificate issued for the new server with the same URL address. This should be different from the existing servers SSL certificate even though the URL is the same. The SSL certificate’s serial numbers will be different between the 2 servers.

I can go ahead and install the new SSL certificate on the new server and test. Then when I am ready, I can point DNS to the new ip address.