Cut the watermelon into 1-inch thick slices using a sharp knife on a cutting board. Ensure the slices are uniform for even grilling.
Brush both sides of the watermelon slices lightly with olive oil using a basting brush. Sprinkle with salt if desired.
Preheat the grill or grill pan over medium-high heat until hot, with visible heat waves and a slight smoking aroma.
Place the watermelon slices on the grill grates or pan, and cook for about 2-3 minutes per side, until grill marks appear and the surface begins to caramelize with slight charring.
Flip the slices carefully with tongs and grill the other side for another 2-3 minutes, ensuring the slices are lightly charred and the flesh appears softer and more translucent.
Remove the grilled watermelon from the heat, let it rest for a minute, then serve immediately, showcasing the smoky caramelized exterior and creamy interior.