The only SNES game of that kind I can think of would be Valis
but the heroine does not hold her skirt.
Maybe one of the Sailor Moon games? (for the outfit)
Could you tell us, if you remember:
- if it was a game in English or Japanese (the question was hidden in Akira's post).
- what kind of sidescrolling it was. Was it more like Valis/Castlevania, more like a beat'em all (double dragon) or more pure platformer (a la Mario)
- if you are 100% sure it was SNES. For the chibi sprites I would think of Syd Valis on Megadrive/Genesis. For the skirt holding I would think of Buletta from Vampire Saviour (not released on SNES, but there is probably a port on Playstation).