Starting with the watermelon squares, push the watermelon to the very tip of the skewer. Then skewer a basil leaf, then a tomato half. Continue with another watermelon, basil leaf, and tomato half. Place the skewer on a serving platter so it stands upright, using the lowest watermelon square as a base. Continue with the remaining skewers.
Drizzle the skewers with the reserved balsamic syrup and the olive oil. Sprinkle with coarse salt and serve.