Bring first 6 ingredients to a boil in a medium stainless-steel saucepan, stirring to dissolve sugar. Reduce heat to medium; simmer 5 minutes.

Using a fine-mesh sieve, strain into a medium bowl; return liquid to pan. 

Add cherries and rosemary to saucepan. Simmer until cherries are tender, 3-5 minutes. Transfer cherries and rosemary to a 1 quart mason jar. Pour in enough pickling liquid to cover cherries. Cover and chill.