Combine sugar, water, and lemon rhind in medium saucepan; bring to a boil. Boil 5 minutes, stirring occasionally. Remove from heat; cool, Remove rhind and stir in lemon juice. Add cherries and juice to syrup. Cover and refrigerate. Syrup may be stored up to a month in the refrigerator.
To make lemonade, pour the syrup into a half gallon container and fill with water, stir. For 1 glass at a time, add 1/3 cup syrup to 1 cup cold water. Serve over ice in a 16 oz. glass.