Heat grill to high heat (about 450°F to 500°F) and oil grates with vegetable oil.
In a small bowl, stir together the sugar, salt, and lime zest.

Lay the watermelon wedges in a single layer on a sheet tray. Reserve 1 teaspoon of the salt mixture; set aside. Sprinkle half of the remaining salt mixture all over the watermelon wedges. Flip and sprinkle the wedges with the other half of the salt mixture.

Place on a cooling rack set over the sheet tray and let rest for 15 minutes. After resting, press the slices firmly with paper towels to remove excess moisture.

Place the wedges on the grill over direct heat and cook for 2 to 3 minutes on each side, until grill marks appear.

When done grilling, place on a serving platter. Sprinkle with the reserved salt mixture, feta, and cilantro. Serve with lime wedges and drizzle with balsamic glaze.