When I was doing the tour of foam suppliers pre MA show, they recommended using an electric carving knife!
I've used an electric carving knife on foam before. It cuts it, but you don't get a particularly clean finish with it. A bandsaw with a knife blade in it, is deffo the best way.
For home use I have a long Sabatier filleting knife which is scarily sharp.
Placing the foam on a surface which has a slot in it, keeping the blade wet, and cutting only on the downward stroke, the blade disappears into the slot, cutting the foam cleanly as it does so - you move the foam towards the cutting edge - rather than moving the blade along the line you want to cut.
For cutting neat holes, I have a dozen or so copper and aluminium lengths of pipe, varying from ~3mmØ to ~50-mmØ.
I've put these inna lathe and taken the wall thickness at one end down to effectively an knife edge.
These tubes can then be hand turned into the foam to core out round holes.
I really should get out, a bit more often.