Client certificate authentication with HTTPSecureSocket

I’m writing an application which have to communicate with a web service which requires client certificate authentication. If I try to communicate with the server without setting the CertificateFile and CertificatePassword properties of an HTTPSecureSocket, I get a normal response stating I have to use a certificate. But if I set these properties appropriately, I get an general 301 HTTP error code which is really strange.

Is it possible to use these propertes in a client certificate authentication process?