A pilgrim's hat. Warburton says, as the chief places of devotion were beyond sea, or on the coasts, pilgrims used to put cockle-shells upon their hats, to indicate that they were pilgrims. Cockles are symbols of St. James, patron saint of Spain. Cockle-scallop, as in heraldry.
And how shall I your true love know From many another one? Oh, by his cockle hat and staff, And by his sandal shoon.
Beaumont and Fletcher: The Friar of Orders Grey.