In a small saucepan, combine sugar, water and rosemary sprigs over medium heat. Stir until the sugar has dissolved, about 3 minutes.
Bring just to a boil, then remove from heat and let cool completely before using or storing. Discard rosemary sprigs. Store in a glass container for up to 1 month.
Rosemary champagne cocktail
Add cooled simple syrup, lemon juice and vodka to a champagne flute. Top with champagne. Garnish with a fresh rosemary sprig.
Notes
For a non-alcoholic version of this cocktail, skip the vodka and use sparkling cider or sparkling lemonade in lieu of the champagne. Prosecco, cava or any other dry sparkling wine can be substituted for the champagne.