Place the fruit on a cutting board lined with parchment. Trim the tops and bottoms of the melons and pineapple and sit them upright on the cutting board. Using a very sharp knife, cut away the rind, slicing lengthwise, working your way around the fruit. Cut about 24 very thin slices of melon in the same fashion, slicing from top to bottom, allowing the juices to collect on the parchment paper.
Slice the pineapple lengthwise into 1/8-inch slices. Pile and cut into matchsticks.
Pour the juices that have collected into a small bowl. Stir in the honey and set aside.
To assemble the fruit sushi, lay the melon slices vertically on the cutting board. Place 3 pineapple matchsticks horizontally at the base of the melon slice and roll. Trim the base so that the rolls sit firmly on a dessert plate. Serve with the honey dipping sauce.