Since there are only a small number of such chips, the emulator will also have a library of cartridges it supports. You emulate those chips the same as you would emulate the CPU or PPU. Sometimes it's easy: the add-on chip is just a regular SNES CPU at a higher clock speed. Sometimes it's hard, because it's some sort of obscure finicky twiddly bits.
The situation is significantly worse on, for instance, the NES, which had 40 or so different chips for bank switching, which is thankfully natively (and therefore uniformly) supported by the SNES.
