Originally Posted by
noglider
WNG, yes, that's it. Rather than a punch, I usually use the side of a wrench, but a punch is good, too.
This is a pretty old school technique... but not many new mechanics know how to do it properly and without marring the brake.
I have some brass rod in varying diameters which serves me quite well and wooden dowel can also be used although it will need to be replaced frequently.
As for fixed cups... the Shelbroco fixed cup remover rarely ever fails.