I just open the live website in a different tab (browser tab, not editor tab) and use keyboard shortcuts to switch between browser tabs. It's the only way that is guaranteed to work. I could try loading the live website in an iframe inside the editor, but it will break if the live website uses X-Frame-Options: SAMEORIGIN and the editor is located on a different hostname (which it really should be for security's sake).
Cool, didn't know about X-Frame-Options. Either way, it'd be cool if there was a good option for when you don't have access to ssh or aren't comfortable with it, which it seems like this could fill.