Although not punching as you requested you could consider a circle
shear. These are used for cutting circles from square blanks for say
metal spinning were you don't usually want a hole in the centre.

Ron Hubbard wrote:

Here, I guess is a newbie question, because I don't remember that part of machine
shop. Does anyone know of a way to punch out nice round circles of aluminum or
brass out of sheet metal in such a way that there are no holes in the circles?

Ron