Generally watermelon will be ready for harvest 45 to 60 days after flowering. Watermelons won't slip from the vine at maturity like that of cantaloupe fruit. So the best ways to identify the ripened watermelons are
a. Rap the fruit skin. If you hear hallow sounds (low-pitched thud) indicates fruit is ripened. The unripened fruit echos high-pitched, tinny sound.
b. Also check for the tendrils near the fruit stem which will become brown and dry at maturity.
c. If you touch the fruit surface it should appear rough and the color of the fruit become dull.
d. The color of the fruit which is touching the soil surface changes from light green to yellowish.
e. Maturity of fruit also increases the waxiness of the rind.
http://extension.missouri.edu/p/M173

It is better not to harvest the watermelon until they become ripen since sweetness of fruit won't increase after harvesting.

Lower temperature delays the ripening process in watermelon. Also the vine is very sensitive to even slight frost (31 to 33 degree F). So using of frost blankets or cold frames to cover fruits and vine reduces frost damage.

According to University of Minnesota, the honeydew melons can be ripened by bagging melon fruits with ripening apple or tomatoes. The ethylene gas released by apple or tomatoes induce ripening in melons.
http://www.extension.umn.edu/garden/y...