Combine the butter, maple syrup, lime juice, cinnamon, and salt and pepper to taste and mix well. (Use immediately or store in an airtight container in the refrigerator for up to 1 week).
Prepare a medium-low fire in the grill.
Peel the squash, cut in half horizontally, remove the fibers and seeds, and slice about 1/2 inch thick.
Steam the squash over boiling water until the flesh is just tender, about 10 minutes. Brush the marinade onto the warm squash.
Grill until grill-marked on the bottom side, about 5 minutes. Check frequently; squash will char easily. If there are hot spots, you may want to rotate the positions of the pieces. Brush with the glaze, turn each slice, and grill until tender throughout and grill-marked on both sides. Remove from the grill, and brush on any remaining glaze. Serve hot.