Tallinn Museum of Orders of Knighthood Old Town

You'd have to be really devoted to phaleristics (the study of medals and military insignia) not to resent the steep admission at this niche museum, but it does have one of Europe's largest collections, and some of the insignia (of the orders of the Garter and the Dannebrog for instance) are exquisitely crafted. Covered by the Tallinn Card.