The closet he came was in the clone wars 2003.... Caught Grievous while taking off, crushed his chest up... but in the actual movies, no they definitely didn't.
Okay sorrry, i was thinking of something else. The real reason they didn't send Anakin is because he was just a Knight, Obi-Wan had lots of training and more experience.
Mace fought Grievous in the Labyrinth of Evil novel. It takes place right before the events of Revenge of the Sith and shows Grievous kidnapping Palpatine.
Mace came close to defeating Dooku in a short duel, but the latter was rescued by MagnaGuards. He later defeated Grievous before using the Force to crush the latter's chest during the attempt to kidnap Palpatine.