For this tangy party drink recipe, use both types of melon so you can serve different colors and flavors of the drink.
In a food processor or blender, combine melon cubes and lime juice. Cover and process or blend until smooth. Press mixture through a fine-mesh sieve; discard pulp. (You should have about 1 cup juice.) Serve over ice or chill mixture and serve in chilled martini or wine glasses. If desired, garnish with melon or lime wedges.