Seed the melon and discard the seed pulp. Cut the flesh off of the rind into roughly 2-inch chunks. Discard the rind. Place half the melon flesh in a large blender or food processor along with 1 cup water, 1/2 tablespoon honey, and 1/2 tablespoon lime juice. Blend at medium high speed until smooth, then empty it into a large pitcher. Repeat with the remaining ingredients and add the desired amount of ice to the pitcher before serving. Can be kept covered in the refrigerator for a couple days.