Preheat oven to 350°. Halve grapefruits and section; remove membranes. Return grapefruit sections to grapefruit halves. Drizzle 1/4 teaspoon rum extract over each. Top each with 1 rounded tablespoon of whipped cream. Place on an ungreased foil-lined baking sheet.
In a large bowl, beat the egg whites, cornstarch and cream of tartar on medium speed until soft peaks form. Gradually beat in sugar, 1 tablespoon at a time, on high until stiff glossy peaks form and sugar is dissolved. Mound 1/2 cup on each grapefruit half; spread meringue to edges to seal. Bake until meringue is browned, 15 minutes. Top each with a cherry. Serve immediately.