Homemade Cherry Soda

Bring cherries, Demerara sugar, and water to a boil in a large saucepan over medium-high heat. Reduce heat to low; simmer, stirring occasionally, 15 to 20 minutes or until cherries are tender. Let stand 30 minutes. Press mixture through a fine wire-mesh strainer into a pitcher, using back of a spoon to squeeze out juices; discard pulp. Stir in lime juice and liquid from jarred maraschino cherries. Chill 2 to 24 hours. Stir together 3 Tbsp. cherry mixture and 1 cup club soda for each serving. Serve over ice in 16-oz. glasses.