what raises the stitching on new era caps?

I use 3MM foam. Bump up the density of your satin stitches. You'll also need to put an "end cap" on an "L" for instance or anything that ends 'open' at the ends. When finished, pick off your foam. You'll see trace reminants of the foam sticking out most likely--run a HEAT GUN (not a hair dryer it wont work lol) over it a couple times on LOW (not high, that melts it) and they should shrink right up.

It's actually puffy foam that gets stitched over. It is a layer of foam that varies in thickness according to how high you want it to look. The design has to be digitized correctly to use foam. Look on you tube there might be a video.