Paul Schreiber blogs about the tech behind the websites of presidential candidates. "So, you want to run a country. Can you hire someone who can run a website? ...Here's how the (declared) candidates' sites fare." There's a table comparing 4 candidates' sites based on HTTPS, URL permutations, IPv6, SSL rating, and other related qualities. Schreiber mentions that he will "update this as more candidates declare or sites change."
From the blog comments
HillaryClinton.com was using IIS (and no https) until Sunday morning, when they switched over.
(Score: 1) by Fauxlosopher on Tuesday April 21 2015, @12:45AM
And therein lies the rub. SSH and HTTPS credential verification are handled in the same fashion, and there's some level of required trust for the vast majority of users who do not have physical or local-network access to the servers they want to use encryption with.
The NSA and CA system are known threats/weaknesses as far as credential verification systems go, so the existing HTTPS-with-CA system can't be pointed to as a proper "existing solution".
Other private alternatives or methods exist, such as "Perspectives" and "Certificate Patrol" as early examples. Some combination of widespread democratic verification and certificate pinning systems are likely going to be required in functional solutions.