Use a serrated knife and cutting board to cut the watermelon into 1-inch thick slices. Remove the rind if desired, or leave it on for easy handling.
Preheat the grill or grill pan to medium heat (around 350°F). Lightly brush the watermelon slices with a neutral oil, such as vegetable or canola oil, using a basting brush or paper towel.
Place the watermelon slices directly on the preheated grill grates. Grill for approximately 2-3 minutes per side, watching for good grill marks and slight browning. Flip using tongs when slices develop visible sear lines and start to release easily from the grill grates.
Cook until the slices are charred with dark grill marks on each side and the watermelon begins to soften slightly, emitting a sweet, smoky aroma.
Remove the slices from the grill and transfer to a serving platter. Optionally sprinkle lightly with salt for enhanced flavor.