Use a sharp knife and cutting board to slice the watermelon in half horizontally. Carefully remove any seeds if desired, then lightly season the cut surfaces with salt. Place the watermelon halves on a plate or tray ready for grilling.
Preheat the grill to medium-high heat. Once hot, use tongs to carefully place the watermelon halves cut side down onto the grill grates. Grill for about 4-5 minutes, or until the edges develop visible char marks and a slight caramelization begins to appear.
Flip the watermelon halves using tongs and continue grilling for another 4-5 minutes on the skin side. During this process, observe the flesh for caramelized, darkened edges that indicate proper charring; the interior should remain juicy and soft.
Remove the grilled watermelon from the grill using tongs and transfer to a serving platter. Allow it to rest for 2 minutes; then, cut into slices or wedges, exposing the smoky, caramelized exterior contrasted with the moist interior.
Optional: sprinkle with additional salt or fresh herbs if desired. Serve immediately while still warm, showcasing the crispy charred edges and juicy flesh.