In the container of a blender, pulse cantaloupe until smooth. Whisk in honey and ginger juice. Gently stir cider into cantaloupe mixture, being careful not to overmix. Pour mixture into a 13×9-inch metal baking pan. Freeze for 20 minutes.

Using a fork, stir icy portions into center of pan every 20 minutes for 1½ hours. Using same fork, scrape mixture into flaky crystals. Cover mixture with plastic wrap, and freeze for up to 3 days. To serve, scrape granita into cups. Garnish with mint, if desired.