Preheat oven to 350 degrees F.
In a mixing bowl, beat egg whites and salt to soft peaks, then gradually add sugar and beat again until peaks are stiff. Beat in vanilla extract. Using a rubber spatula or wooden spoon, stir in half of the coconut. Sprinkle in the nutmeg and flour, stir, then fold in the remaining coconut.
Using a melon baller or other small scoop, form 12 mounds a couple of inches apart on baking sheet. Bake cookies for 12 to 15 minutes, until lightly golden. Remove from oven and garnish each cookie with half of a cherry. Transfer to a rack to cool completely.
Nutrition Information:
81 Cal., 3 g. fat, 0 g. fiber