A lot of emulators have online play, the ones I'm familiar with are Project64k/Mupen64k, Dolphin also has online play which i haven't tried, I believe melonDS does as well.
You can get online working in SNES games as well, but at some point online was broken/removed in both ZSnes and Snes9x, and I don't think it was ever added back, so you may have to use an older version of those emulators to get it working, unless Retroarch or Higan have online play.