In a large bowl, stir together the grapefruit juice, ginger ale, sugar and grenadine until the sugar is dissolved. Pour into a 9-by-13-inch metal baking dish and freeze for 2 hours. Using a fork, scrape the surface to break up the ice, then freeze for 2 more hours.
Scrape the surface again and divide the mixture among 4 chilled glasses; top each with a cherry. Serve immediately.