For the NES there is now the HiDefNES kit. Which you can get your NES modded with that will output 1080p over HDMI.
The kits are available at
https://www.game-tech.us/ and they also reccommend installers over there.
Here's a video showing what its like
https://youtu.be/TI60A3DpI6w
There is also the option of having your NES RGB modded and picking up an upscaler like the OSSC or Framemeister. That will be the more expensive route but they'll work with more than just the NES. The HiDefNES kit is obviously just an NES solution.