Position racks in the middle and lower third of the oven; preheat to 200 degrees F. Line 2 baking sheets with parchment paper. Combine the pomegranate molasses and food coloring in a small bowl.
Beat the egg whites and cream of tartar in a large bowl with a mixer on medium speed until foamy. Increase the mixer speed to medium high and beat until thick and opaque, about 1 more minute. Gradually add the sugar and beat until stiff shiny peaks form, about 3 more minutes.
Drizzle or brush the pomegranate mixture in a thick line along the inside of a pastry bag fitted with a large round tip. Carefully fill the bag with the meringue. Pipe about 12 swirls of meringue on each baking sheet. (The meringue may be slightly pink at the end of the bag.) Bake, switching the pans halfway through, until the meringues are crisp and dry, about 3 hours. Let cool completely on the baking sheets.