I know the PSP has the capability of running emulation, but now that the 20 year patents for the SNES & NES hardware are up there are a couple of devices out there that will allow portable playing of old cartridges:
Supaboy (SNES only)
Retro Duo Portable (SNES; NES & GEN with adapters)
There is something to be said about playing directly from the old carts, even if it is on a new portable system. My first thought went to the Ancient Cave in Lufia 2 handheld off of the original cartridge…
Some of the reviews are showing they haven’t perfected these machines quite yet (unshielded speakers on the Supaboy, etc), but maybe in a year or two the revisions would be fun to give a try.