When checking for ripeness, depress the blossom end of the melon, opposite the stem end, to make sure it is not hard and yields slightly when depressed. And, the sweet aroma of the melon should be detectable. To ripen, place the melon in a paper bag at room temperature. To store, place ripe melons uncut in a plastic bag to be refrigerated for up to a week. When serving, add a little lemon or lime juice to enhance the flavor of the fruit.