Line a large rimmed baking sheet with wax paper. Spread out 1 quart seeded watermelon chunks and freeze for 2 hours or freeze overnight. (If freezing overnight, put chunks in a large plastic bag first.)
In a small saucepan, cook 1/2 cup sugar and 1/4 cup cold water over medium heat, stirring, until sugar is melted. Stir in another 1/4 cup cold water, let cool, then stir in 3/4 cup fresh lime juice (5 to 6 limes).
Blend melon and lime mixture in 2 batches. Pour into glasses. Garnish with melon or lime wedges.