Since we're mainly concentrating on france in the 14th century, we have a smiliar result: there are hardly frilled coifs in french headwear 1340-1400. There are several different shapes of veils and babières, crespinettes and such, but hardly frilled ones; however, frilled headwear appears earlier in the 13th century, the classical "Gebende" in french manuscripts is often frilled.
I'll look into our collections, maybe we'll have some additional examples for you.