Indentation on a Patent Leather Shoe

A wooden shoe stretcher might do it. They're meant for making too-small leather shoes fit correctly. They also force the shoe to hold its shape when there is no foot in it.

Or just wait until a nice warm sunny day and put them outside to bake for a while.

Since most - if not all - patent leather shoes are actually plastic nowadays - you could try gently heating the spot with the dent and then trying to straighten it out by stuffing that part of the shoe with tissue paper or something similar.