The barbette, or "little beard" is a chin band worn with many medieval head coverings. A fillet, or small circlet of stiff cloth, was a common accessory. So was a veil.
This is a picture of a 14th Century barbette and fillet
taken from the Manesse manuscript, which is dated around 1330.
We bought the fillet from Angevin Treasures, and the barbette from another vendor at an SCA tournament.