In a Final Fantasy VI "natural magic" run, you can only use the magic characters gain by leveling up. So that means no equipment that allows characters to learn magic, or Espers. Apparently leveling stat boosts through Espers are also not allowed. While this challenge is fairly straightforward, it can be combined with other challenges such as the CES challenge (Celes, Edgar, Setzer challenge), which requires that you use only the aforementioned characters unless the game forces you to use others.
This challenge really is a good excuse to pick up this classic game again.