Emulators (Chrono Trigger)
While the Compendium cannot host ROMs, it can link to the emulators that run them.
ZSNES has historically been the most popular SNES emulator.
Snes9x is an open source editor.
For exceptional graphics, get a build with XBRz:
For the most technically-accurate, frame-perfect, hardware-recreating emulator out there, try higan.