The New Liturgical Movement has recently had two photographs of surviving medieval conical chasubles, both handsomely decorated with royal heraldry. There is this spectacular example from Spain:
Chasuble of the Archbishop of Toledo,
Don Sancho de Aragón (1264-1275)
and from fourteenth century France there is this example from the church at Brienon:
It is decorated with the arms of Blanche de Navarre Queen of France (c. 1333 - 1398) also known as Blanche d'Evreux, daughter of Philippe of Evreux, King of Navarre who became the second wife of King Philippe VI (1293 - 1350):
The arms are: Party per pale: 1. France. 2. Party per fess: a. Navarre. b. Evreux.
I posted about Queen Blanche in my post The library of a fourteenth century Queen of France in September last year.
Fr Blake has some observations about this form of the vestment in his post Conical Chasubles.