Not just in the sense of running DSi games faithfully: a good reproduction of the DSi environment is also useful to would-be homebrewers.
You might have noticed that one of my goals for the 1.0 release is to get DSi mode in melonDS up to par with DS mode. If you're running into trouble: Howto/FAQ While it is still a work in progress, it has a pretty solid set of features:
MelonDS aims at providing fast and accurate Nintendo DS emulation.