Cut the rind from the 6- to 8-pound watermelon and discard. Cut the flesh into 2-inch cubes (you should have about 13 cups).
In a blender combine about one-third of the watermelon cubes and one-third of the water. Cover and blend until smooth. Strain through a fine-mesh sieve into a pitcher or large glass jar. Discard solids. Repeat twice, using remaining watermelon and remaining water.
Stir lime juice and the 2 tablespoons honey into strained watermelon mixture. Serve immediately or chill until ready to serve.
Serve in ice-filled glasses. Garnish with lime wedges and watermelon slices; serve with additional honey, if desired.