Get a PSP, it can emulate EVERYTHING below N64, but it does emulate the PS1 without issues.
Also, i had an Xperia Play, can emulate everything under PS1, including PS1.
It's because the PSP doesn't just emulate PS1 games but it's CPU architecture is so close to that of the PS1's R3000 that it can run some of the original instructions nativley and everything else gets taken care of with emulation.
A fun little tidbit that points to the origin of POPSloader(the PS1 emulator on the PSP/PS2 that handles what the CPU can't) is that it shares some emulation glitches with a PS1 emulator for the Macintosh that existed in the early 2000s...one that sony bought the rights to in order to take it off the shelves.