I've always wanted to do one of these, and I finally got around to it.
A while ago I realized that I'm really accumulating quite a few site tokens (SO SHINY SO PRETTY). I also noticed that they really remind me of pilgrim badges. I decided I'd like to come up with a way to display them that's at least plausibly period rather than just hoarding them. I like hats, plus I found this great picture:

I settled on a hat. I could (and probably should) have just bought a floppy felt hat, but I've been having so much fun making hats lately that I decided to go for it. I found
this record of a hat from Herjolfsnes and decided that a pillbox shape would be easy to sew. (In fact I ended up bombing the shape pretty royally, but I've decided to ignore it rather than pull it apart and fix it.) This hat is washed (felted) wool lined with cotton twill. The trim is I think silk (it's been sitting in my collection for a long time).
This would be a very easy project -- you just need a strip of fabric 10 cm wide by the circumference of your head long and a circle of fabric with this same circumferece. Add seam allowances. If you want to line it, make another set of strip and circle in your lining fabric. Sew the outside parts together, sew the lining parts together, and sew the two sets together (inside out), leaving a gap in the seam so you can turn the hat right side out. Turn the hat. Sew on the trim (which will close up your hole).
After assembling my hat I sewed on my "badges", not paying particularly close attention to how evenly I spaced them, and voila!
This style of hat probably isn't even close to acceptable for my persona -- but it looks WICKED cute over a big sheer veil. Pictures of me wearing it soon, I hope.
My dad said "It's like a Girl Scout merit badge sash, but for your head!" which I think is a pretty good description.