Puree the cantaloupe with the cider, the juice of 1/2 lemon (or to taste) and a pinch of salt in a blender on low speed. While you want the mixture to be smooth, keeping the blender on low will help you avoid whipping unnecessary air into the melon and lightening the flavor along with the color. Add a little ice water if the blender has trouble blending the melon, and if you feel the melon lacks sweetness, add honey to taste. Refrigerate until ready to make the drinks.
Put half each of the melon puree and gin, and 1 more tablespoon lemon juice in a shaker (or any container with a fitted lid) with a few ice cubes and shake until blended and cold. Strain into 2 chilled glasses. Rub the rim of each glass with the lemon wedge for a little added acidity when sipping, and garnish with melon balls. Repeat to make 2 more drinks.