Cut the rind from the whole watermelon, and discard the rind. Cut the watermelon flesh into 2-inch cubes.
In a blender, combine about ⅓ of the watermelon cubes and ⅔ cup of the water. Cover and blend until smooth. Strain through a fine-mesh sieve into a large pitcher or large glass jar; discard the solids. Repeat twice, using the remaining watermelon cubes and water.
Stir the lime juice and honey into the strained watermelon mixture. Serve in ice-filled glasses. Garnish with watermelon wedges, and float lime slices in the glasses.