Rim 3 cocktail glasses with juice from a grapefruit wedge; dip in coarse sugar or salt, giving a gentle turn in each direction to coat the glasses.
In a liquid measuring cup or cocktail shaker, combine grapefruit and lime juices, liquor and simple syrup. Mix or shake well to blend. Fill glasses with crushed ice.
Pour 1/4 cup club soda into each cocktail glass. Top off each equally with the grapefruit mixture. Garnish with grapefruit wedges, if desired.
*To make simple syrup, combine equal parts sugar and water in a small saucepan over medium heat. Heat, stirring occasionally, until the sugar is fully dissolved. Chill before using. Use to sweeten coffee, cocktails, etc.