Bring the water and sugar to a boil in a small saucepan over high heat. Stir in the rosemary, and set aside to steep for 1 hour.
Place half of the lemon juice, and half of the watermelon into a blender. Strain the rosemary syrup through a mesh strainer into the blender. Cover, and puree until smooth. Strain into a jug, then puree the remaining lemon juice and watermelon. Refrigerate till cold. Stir the drink before serving over ice.