Choose a Ripe Melon Watermelon season lasts from May to September and peaks from mid-June to August. They taste best when fully ripened and served icy cold. A good watermelon should be symmetrical, with a deep green rind. A yellow spot indicates where it rested on the ground during ripening. The rind should be smooth and dull, free of cuts, dents and bruises, and give just a little under pressure. You should hear a deep, hollow thudding sound when you thump it. If buying cut watermelon, look for bright red flesh with dark brown or black seeds. Avoid slices with white streaks in the flesh. Slices should be tightly wrapped. Storing Watermelon Whole watermelons will keep in the refrigerator for up to one week. Cut melon may keep up to two or three days when tightly sealed with plastic wrap or stored in airtight containers to prevent drying. Don't refrigerate at temperatures below 40°F, as chilling injury will occur.