Peel the watermelon and cut into slabs, like fillets. Using the most seedless portions, cut watermelon flesh into 1 1/2-inch cubes. Using a small melon baler or a demi-tasse spoon, hollow out a depression in the top to form a little cup.
Peel and roughly cut up the kiwis. Place the pieces in a blender or food processor with the lime juice and the sugar. Puree then strain out the seeds. Add a few seeds back to show it is kiwi. Place watermelon cubes on a platter and fill the depression with the kiwi puree. Serve cold and lightly sprinkled with course salt, and eat with your fingers!