Tarragon Syrup for Limeade

In a medium saucepan, combine sugar, tarragon, and 2 1/2 cups water; bring to a boil over medium-high heat. Cook until the sugar has completely dissolved, about 1 minute. Remove from heat; let stand 30 minutes. Remove and discard tarragon sprigs. Store syrup in an airtight container, refrigerated, up to 2 months.