Make the rosemary simple syrup: Combine sugar and water in a small saucepan. Bring to a boil, stirring until sugar dissolves.
Add 1 sprig of rosemary to the syrup. Remove from heat and let steep for 15 minutes.
Strain the syrup and refrigerate until cool.
Blend the watermelon chunks until smooth. Strain through a fine-mesh strainer.
In a cocktail shaker, combine 1 cup watermelon juice, 2 tablespoons rosemary simple syrup, and 1 tablespoon lime juice.
Add ice and shake well for 15 seconds.
Strain into tall glasses filled with ice. Top with club soda.
Garnish with fresh rosemary sprigs and watermelon wedges.