When choosing a melon from those that have already been harvested, look for a clean, dish-shaped scar. Also, ripe melons have a pleasant, musky aroma if the melons are at room temperature (not refrigerated).
Watermelons can be more difficult and growers often use several techniques to tell when to harvest.
1. Look for the tendril that attaches at the same point as the melon to dry and turn brown. On some varieties this will need to be completely dried before the watermelon is ripe. On others it will only need to be in the process of turning brown.
2. The surface of a ripening melon develops a surface roughness (sometimes called “sugar bumps”) near the base of the fruit.
3. Ripe watermelons normally develop a yellow color on the “ground spot” when ripe. This is the area of the melon that contacts the ground.
Honeydew melons are the most difficult to tell when they are ripe because they do not “slip” like muskmelons. Actually, there is one variety that does slip called Earlidew, but it is the exception to the rule. Ripe honeydew melons become soft on the flower end of the fruit. The “flower end” is the end opposite where the stem attaches. Also, honeydews should change to a light or yellowish color when ripe, but this varies with variety. (Ward Upham)