Place the watermelon chunks on a plate and freeze them. Reserve a few in the refrigerator if you plan to use them as a garnish.
For the syrup, combine the water and sugar in a small saucepan over moderate heat. Stir until the sugar dissolves. When the syrup begins to boil remove it from the heat and stir in the basil leaves. Cover and allow the syrup to steep for at least an hour. When you’re ready to make your cocktails, strain the syrup and discard the leaves.
In a small pitcher, stir together the watermelon puree, tequila, triple sec, basil syrup, and lime juice.
Combine the sugar and salt on a small plate or saucer. Wipe the rim of each glass with a wedge of fresh lime, and dip it into the salt-sugar mixture to coat.
Fill the glasses with frozen watermelon chunks or ice or a combination of the two and pour the margarita mixture over the top. Garnish with fresh watermelon, lime wedges, and fresh Thai basil sprigs.