if you're talking about the certificate you're using to run your own HTTPS server, then check the config file of your Apache server (probably /etc/apache2/vhosts.d/ssl.conf) for the "SSLCertificateFile" and "SSLCertificateKeyFile" statements - the former points to the currently used public certificate file of your server, the latter to the corresponding private key file. There's no need to "export" that key - you can simply copy the file(s) to the new server and adjust the SSL configuration there accordingly.

Typically, the certificate is bound to the DNS name of the service, as used by the client to connect to the server. But I assume that you are moving the https service from one machine to the other and will change the DNS entry (or NAT entry or whatever) to set that straight.