Cheddar is the go-to cheese for a classic ham and cheese sandwich. Its sharpness cuts through the sweet honey glaze and balances the saltiness of the ham. Cheddar is not a pedestrian choice; there are several high-end cheddars available with sophisticated flavor profiles. Opt for a bandaged cheddar or just a well-aged artisan cheddar from Wisconsin.

Emmentaler is a semi-hard alpine cheese from Switzerland -- in other words, the true Swiss cheese, down to the characteristic holes. It has a slight sour bite that deftly offsets the sweetness of a honey-glazed ham. Similar cheeses include Gruyere and Jarlsberg.

Camembert is a soft and creamy French cheese with slightly sour or pungent flavor notes. The creaminess complements ham's saltiness and marries well to the honey flavor of the glaze. This is a rich, almost decadent pairing. Brie is similar to Camembert and can be used in its place.

Gorgonzola is a blue cheese from Italy. The blue veins that mark its surface are caused by mold and provide a pronounced pungent bite. Gorgonzola plays off sweet flavors, including the glaze of a honey ham, remarkably well. Opt for one that is creamy and not too salty. You can also explore such blue cheese varieties such as Roquefort, Stilton or one of the many high-quality American blues.