Place watermelon cubes in a blender. Cover and puree until smooth. Strain through a fine-mesh strainer set over a large bowl, pressing juices through with the back of a spoon. Discard solids.Advertisement
Add wine, brandy, triple sec and sugar to bowl; whisk to combine. (You may want to add a little more sugar, depending on the sweetness of the watermelon.) Cover and chill at least 4 hours or overnight.
Just before serving, add ice to 2 large pitchers. Stir contents of bowl, then divide between pitchers (or keep half chilled). Divide lime slices between pitchers, and tuck in a few watermelon wedges. Serve, garnishing each glass with a watermelon wedge.