Yesterday, we had a meeting at CAcert Berlin where I had a little talk about how to almost-perfectly configure your HTTPS server. Motivation for that was the very nice Qualys SSL Server test, which can remote-check your SSL configuration and tell you a bunch of things about it.
While playing with that, I created a test setup which passes with 100 points in the Qualys test. However, you will hardly be able to access that page, which is mainly due to it's exclusive support for TLS 1.2. All major browsers fail. Someone from the audience told me that the iPhone browser was successfully able to access the page. To safe the reputation of free software, someone else found out that the Midori browser is also capable of accessing it. I've described what I did there on the page itself and you may also read it here via http.
Update: As people seem to find these browser issue interesting: It's been pointed out that the iPad Browser also works. Opera with TLS 1.2 enabled seems to work for some people, but not for me (maybe Windows-only). luakit and epiphany also work, but they don't check certificates at all, so that kind of doesn't count.
It's basically not the webkit part, but openssl. If a browser uses "plain" openssl without doing anything further and if openssl is on version 1.0.1, it should "just work". Simple textmode browsers like w3m and lynx also do it.