How to Make It
In a small saucepan, combine the sugar with 1/3 cup of water and bring to a boil over high heat, stirring, until the sugar dissolves. Transfer the syrup to a blender or food processor, add half of the watermelon cubes and the lime juice and pulse until smooth. Add the remaining watermelon cubes and blend until smooth.
Pass the puree through a coarse strainer, pressing down on the solids. Transfer to a 9-by-13-inch nonreactive baking dish and freeze, stirring every 30 minutes with a fork, until all the liquid has frozen completely, about 3 hours. Spoon the granita into tall glasses or bowls and garnish with the melon wedges.