It usually causes my whole computer to freeze up and need to be restarted.
I stopped playing ds emulator games,because its bad for my computer to be restarting so much.
All I can suggest is check the help file that might have come with the emulator and see if there is any known bugs with FF titles on it – usually emulator authors will try to fix such bugs and try to get games running on them if they don’t, but it might be a while before that happens.
EDIT: okay, I’ve recently tried a DS emulator on my system (DeSmuME) and although I haven’t tried either FFIII or IV DS on it yet (I’ve only played Castlevania Portrait of Ruin with it so far, which runs at half speed and the sound/music is glitchy), I think it might just be indeed a case of the emulator you’re using might just not be compatible with those games yet. Try using another emulator and see if that helps.