I noticed that if you try to add an SSL certificate monitor on a host that requires client certificates for a connection, the monitor does not function, instead claiming that SSL is not supported by the host—a configuration error.

While it's true that the monitor wouldn't be able to connect to such a host without a client certificate, it should still be able to read server certificate information, and thus fulfill the intent of the SSL certificate monitor.

Alternatively, Site24x7 could add a feature by which you can associate a client certificate with an SSL certificate monitor (Website checks have this capability).

I called up the support number and chatted with a representative about this, and he confirmed that indeed, currently, SSL certificate monitors don't support hosts that require client certificates.