You could have a URL format that includes the signature of the key. Big sites would transparently add the signature and the browser would give a warning if the signature is different. You could add the same signature information to cookies and warn the user if it changes.
There is a big tradeoff here: The ability to enter URLs manually.
This is what we tell users to do today for important sites, and not click in links in mail or elsewhere. It is not obvious that there is a net benefit in security.
