In the last post I showed what we should expect from theory - and the observations agree nicely with it. In UV and blue the shape of the transit is much rounder than for longer wavelength. Indeed, limb darkening is stronger for shorter wavelengths.
It is actually pretty hard to measure the limb darkening of stars; they are just too far away to spatially resolve them. Analyzing exoplanetary transits is one of the best methods to verify whether the theoretical predictions are really correct. And so far the models seem to work pretty well - although in detail observations and theory are not so easy to compare. After all, the exact shape of the transit depends on a lot of different things.