Place sugar and 1/2 cup water in a small saucepan over medium-high heat; bring to a boil. Reduce heat, and simmer 3 minutes. Remove from heat. Place sugar mixture in a small bowl; cool 10 minutes. Cover and chill at least 30 minutes.
Place sugar mixture, watermelon, and juice in a blender; process until smooth. Pour watermelon mixture into an 11 x 7-inch baking dish; cover and freeze 3 hours. Stir well. Cover and freeze at least 2 hours or overnight. Remove mixture from freezer, and let stand at room temperature for 10 minutes. Scrape the entire mixture with a fork until fluffy. Serve with lime wedges, if desired.