I've read a few threads on here about folks hunting for 70's and 80's Trek head badges and having not much luck. About the only sources are VELOCALS vinyl decal or trying to find someone on ebay with a take-off from another bike (Meaning someone else will be looking to replace the one on that frame later) ... but I digress.
My approach was to use some 0.015" brass shim stock (local hardware store) that's thick enough to hold up but thin enough to work easily. I searched the web for images of badges and copied multiples and printed several in the 2" size range. I cut out the badge with shears and used a sharpie, a compass and Xacto knife to lay out the general design.
I have a jewelers saw and a few basic engraving tools (From a prior blackpowder rifle building project) and drilled out pilot holes where I was going to saw (Note this is a departure from the original badge... but wtf it's MY bike, right!?
After careful cutting and filing with jewelers files I then Engraved the TREK lettering. Just to let you know my engraving SUCKS, but I just wanted to have a little relief & roughness where the paint could sit flush with the surface. When it was all done I buffed it and then curved it using a dowel and a 3" piece of PVC pipe cut in half long-ways as a die. ( I did have to do a little hand bending to get it just right). I elected to glue in place with some E6000. Not "perfect" but not bad from about 2' away
