How can I update my certificate for a secure connection?

You need to talk to the router manufacturer for that. They control every aspect of its web interface, including the SSL certificate. You likely have no access or control to that detail.

Usually it's automatically installed/updated as part of any firmware updates for the router. Make sure you're using the latest version.

If you are, and the manufacturer isn't updating it any more, then you're going to have to live with the warning message until they fix it, or you get a different router.

Are you asking about a router's embedded web server? If it requires an updated security certificate, it would most likely be issued in conjunction with a firmware update. The same general principle applies to its embedded web server. Does that help? Who makes that router?

Only website developers can update their website security certificates.