1. Stir together the sugar, water, and rosemary sprigs in a small saucepan over medium. Bring to a simmer, and cook, stirring, and gently muddle the rosemary with a wooden spoon, until the sugar has completely dissolved, about 1 minute.
2. Remove from the heat, and cool to room temperature, about 20 minutes.
3. Strain into a small, airtight container, discarding the rosemary, and refrigerate for up to 2 weeks.