Using a very sharp knife, slice the rind from the bottom of each watermelon half. The halves will now lay flat on a cutting board.
Working from top to bottom, trim the rind from the watermelon flesh in 4 cuts, creating 2 large squares. Cut each square in half to make 4 smaller squares. Cut the squares vertically into thirds. Rotate counterclockwise and repeat the cut. Rotate once more counterclockwise and cut into thirds again.
Place on dessert plates and serve each with 2 tablespoons of Campari, if desired.