Melons will have the highest sugar content if allowed to ripen fully on the vine.
When cantaloupes are ready for harvest they will easily separate from the vine. Put a little pressure on the fruit where the vine attaches. If ripe, the fruit will slip off the vine and you will see a dish-shaped depression on the fruit. Twisting the stem to force separation indicates the melon is not ready. Additionally, the skin of the melon should begin to show yellowing instead of solid green during immaturity. A ripe cantaloupe should have a musky fragrance and the end of the fruit opposite where the vine is attached should be soft. Cantaloupe can be stored in a refrigerator for two weeks.
Watermelons display their readiness to harvest as the underside of the fruit changes from green-white to yellow. The glossy green that was once apparent on a majority of the fruit will also become more dull. The tendril attaching the fruit to the vine will turn black when the fruit reaches maturity. Separate the fruit from the vine by cutting the tendril leaving about two inches still attached to the fruit. Store freshly harvested watermelons at room temperature for one week or in 50-60 degrees F for two to three weeks.
Honeydew melons do not easily pull away from the stem when ripe. Instead, rely on the change in color of the fruit from pale green to light yellow, the softening spot on the fruit opposite from where the vine attaches and the aroma coming from the fruit. Honeydews can be stored for two weeks at 50 degrees F.
Cynthia Domenghini, Extesnion Agent