In a small saucepan, bring 2 cups water to a boil; add rosemary sprigs. Reduce heat; simmer, covered, 10 minutes.
Remove and discard rosemary. Stir in sugar and honey until dissolved. Transfer to a pitcher; refrigerate 15 minutes.
Add lemon juice; stir in cold water. Serve over ice. If desired, top with additional lemon slices and rosemary sprigs.
