Get yourself a SNES emulator (ares is the best standalone one nowadays, but you can also use RetroArch with the bsnes-jg core if you want to use fancy CRT shaders), then look for a No-Intro SNES set on archive.org (or Minerva if you don't mind torrenting), and you can find Chrono Trigger there. I'd recommend avoiding the PC version if you can. It has some bugs, some weird graphical anomalies, the newer translation (which is more accurate, but I find to be less impactful), and the extra cruft I was talking about.

For Chrono Cross, there's either the PC version (which is just the original running in a glorified emulator), or you can download an emulator and look for a Redump PS1 set on either of the same two sites I listed above to find the ROM. As for emulators, Duckstation is the most advanced one when it comes to enhancements, but you should note it is no longer open source due to some developer drama, but it is still source-available under a non-derivative, non-commercial license (so forking and selling isn't allowed). If you're looking more for accuracy to original PS1 hardware and/or for fancy CRT effects, I recommend Beetle PSX inside of RetroArch (not Beetle PSX HW, which I find to be a lot buggier).

Personally, I recommend Snes9x as an emulator (I also play on linux, Ubuntu if that's helpful). As for hunting down ROMs, you can often find compilation "best of" packages on Archive.org or if you hunt around for trusted sites (I'm unsure of the rules here if I'm allowed to direct you to said trusted sites or not) I'm sure you can find it.

Officially, Chrono Trigger is on Steam and that probably takes minimal finageling nowadays even on Linux.