The tendril where the stem of the melon hits the vine should be completely brown. The melon should also have a nice yellow bottom where it sits on the ground. You can thump it if you like. I never was sure what I could learn from that but its fun ......
The only way to tell if a melon is ready is pick it and cut it open. If in doubt...... wait.
Gardening at 5000 feet elevation, zone 4/5 Northern Utah, Frost free from May 25 to September 8 +/-