Wearing gloves, peel as directed above:
Cut into 1-inch chunks and transfer to a food processor or blender along with:
Puree until smooth. Taste and, if desired, add more lime or orange juice. Transfer to a bowl, cover, and chill at least 1 hour. Halve, seed, cut into wedges, and remove the rinds from:
Set a melon wedge on each plate and spoon a ribbon of sauce over it.