I just upgraded Emacs on my Windows 10 machine from 24.5 to 25.1. For Emacs 24.5 I had GnuTLS correctly setup and for 25.1 I did what I thought I remembered I did:
Got prebuilt Emacs binaries from the GNU Emacs website's download page. I'm using 32 bit Windows, so I got the i686 version of Emacs.
Got a copy of GnuTLS from ezwinports and extracted the zip file to the same directory as Emacs --the way the gnutls zip is organized means that this way both the dll's and the exe's for gnutls wind up in the same directory as the Emacs exe's. (I got version 3.3.11 this time; I don't remember what version of GnuTLS I had when I had version 24.5 of Emacs.)
That didn't work this time.
nil, the package manager is only able to connect to http repositories and not https ones, eww can't handle https either.
How do I setup GnuTLS for Emacs 25.1? Am I misremembering what I did for 24.5? Maybe the binaries from the GNU Emacs website are compiled without GnuTLS and for 24.5 I actually got binaries from somewhere else...