In a small bowl, combine agave nectar, oil, 1 tablespoon lime juice, and cinnamon.
Cut each pineapple half lengthwise into 4 long wedges; cut each wedge in half crosswise. You will have 16 pieces.
Prepare grill on medium heat. Lightly brush pineapple with marinade.
Grill on a rack set about 6 inches over glowing coals. Turn; brush second side with marinade and grill until tender and golden, about 5 minutes per side. Pineapple may also be broiled by placing 4 inches below broiler in oven for about 10 minutes, turning occasionally until lightly browned.
Brush with rum and sprinkle with lime peel. Serve hot or warm.