Trying to up your cocktail game? If you're no longer looking for a new rhum Agricole or some artisanal bitters to set your shelves apart, maybe it's time to turn an eye to your freezer. The difference between a good drink and a great drink isn't just about the booze—it's about the ice.

The recent resurgence of classic cocktails has spawned a concurrent trend of ice appreciation. High-end cocktail bars are shaking, stirring and serving their $18 drinks with dense, extra-large cubes, hand-cut shards and spheres. And there's...