Heat oven broiler. Trim the ends of grapefruit halves so they sit flat when upright; transfer to a baking sheet cut side up. Run a knife around edges and between segments of grapefruit to loosen them. Brush 1 tbsp. rum over each half and sprinkle each with about 1 1⁄2 tbsp. sugar. Dust with cinnamon and cayenne; place 1 cherry in the center of each grapefruit. Broil, rotating pan as needed, until bubbling and slightly caramelized, 5–6 minutes.