I've already mentioned this on another thread here on Vogons, but it's definitely more relevant here. In short, I've managed to get a Wayback Machine proxy working. Here's a screenshot of idsoftware.com from ~2000 running in Netscape Communicator 4.08 in Windows 3.11. It's a Pentium 133 machine with Intel PRO/100 network card. The TCP/IP is being provided by Microsoft's TCP/IP-32 3.11b stack.

I have a tiny computer (an older Intel NUC, actually) running Ubuntu as my FTP server for all my retro machines. I've installed NodeJS and downloaded vintage-proxy on it. Then I've ran the server and configured Netscape to use my NUC as an HTTP proxy over port 8080.
After that I can enter an URL into Netscape and have my NUC respond with a saved page from Wayback Machine. The whole thing runs nice with a few caveats:
- no dynamic content. Stuff like jsp and asp pages doesn't work (because WaybackMachine can't possibly store them), same goes for Flash as far as I can see. So it's kind of better to set an earlier date in server.js (say, 1996 instead of 2000). If WaybackMachine doesn't have a copy for 1996, the proxy will revert to a later date until it finds something;
- it's kind of slow. There's a significant delay in response and the transfer speed isn't great. I like to think that this makes my experience more "authentic" 😀;
- Netscape does crash quite a bit. I think a newer Windows with a more modern browser would work better, but I'm currently interested in Win3.11;
- Cyrillic doesn't work. I've tried opening Yandex.ru (Russian search engine) and Fargus.com (the biggest Russian game publisher of the 90s), but could not get the text to show properly no matter what encoding I chose.
Still, the whole thing feels pretty magical to me.