Make cilantro syrup: Bring sugar and 1/2 cup water to a boil in a saucepan. Remove from heat, add cilantro sprigs, and let steep 5 minutes. Strain, discard sprigs, and let cool.
Stir together seltzer, lime juice, and 10 to 12 tablespoons syrup in a large pitcher. Serve over ice, garnished with cilantro and lime.