Thump it with your finger or thumb. If it sounds nice and hollow, it's ripe.

if you squeeze it and it's hard as a rock or super mushy, it is not ripe. but if you put a ton of pressure on it, and it finally caves in a little, that bad boy will be so smooth and sweet!!! *NOTE* this is in addition to thumping on it. remember-its a 2 step process...listen for the hollow sound, and feel for the tenderness... i work in a restaurant and i can tell you for certain, the apearance has nothing to do with the taste...cuz sometimes the most oddly shaped and discolored honeydews have the most rockin flavor and color on the inside. (but that does not mean pick up all the disfigured ones...cuz sometimes you CAN judge a book by its cover.)

Depends on if you are talking about the true Honeydew or the American Muskmelon variation. On the classic, you will feel and smell the base where the stem was. Should smell sweet and have a slight give. The skin should be slightly waxy. The American variety, you will be looking for the hollow echo sound, and it should be very firm with a bit of give.

It tastes nice and sweet!!!!!

Sorry to be so late answering. I was going to ask this, but when I checked to see if it had been asked I found this thread. Having found it, I felt compelled to search Google and get a good answer. First, the wittiest answer. On the Freethought Forum Angakuk said, "The same way that you test any melon. Hold it up to your ear and tap on it. Do this with several melons and then pick one at random and hope for the best." I've personally found the tapping method useless in choosing good Honeydews and cantaloupes, so I appreciated that advice. Seems only watermelons respond favorably to the tap test. What does ring true is this advice. Honeydews should have light yellow, cream or nearly white skin when ripe. If there is still a hint of green, it's not there yet. When ripe, the melon should be slightly soft to pressure. If it's still hard, it's not ripe. If soft, it's past its prime. Before fully ripening, there are tiny green veins, particularly around where the fruit attaches to the vine. Wait till those disappear. Finally, a ripe honeydew should have a strong floral bouquet, especially around the spot where it attaches to the vine. Happy summer melons!