Make a basket by cutting wedges from both sides of upper half of honeydew, leaving a 3/4-inch strip between the wedges for a handle. Handle should remain attached to lower half of melon. Remove seeds carefully.
With a melon ball cutter, form balls from the lower half of melon, hollowing out entire lower half, and from the cut out wedges. Cut balls from halves of cantaloupe. Trim inside the melon handle with a knife.
Return the balls to basket, arranging them to show contrasts in color. Pour wine over balls. Chill thoroughly.
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