I'm not quite sure what your use case is. If you are just trying to "check ahead of time" before you provide a link to someone for another website then the other answers here will be more relevant than mine.
If you are expecting mysite.com to use an SSL certificate that isn't trusted by default in the browser but you have another way of knowing it should be trusted, then you could use a JavaScript TLS implementation to make cross-domain requests to that other site. However, this requires that your website be served on https and trusted in the browser to begin with and the other site to provide a Flash cross-domain policy file.
If this sounds anything like what you want to do, check out the opensource Forge project:
http://github.com/digitalbazaar/forge/blob/master/README