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.”