Look the watermelon over.  You are looking for a firm, symmetrical watermelon that is free from bruises, cuts or dents.
 

Lift it up.  The watermelon should be heavy for its size.
 

Look at the underside of the watermelon.  It should have a creamy yellow spot from where it sat on the ground and ripened.
 

You cannot tell if a watermelon is ripe by thumping, however thumping can tell you if it is overripe or bruised inside.  Find one with a low toned ring and reject any with a dead thump when you slap it lightly.

Cut the watermelon in half, then in quarters.
 

Cut through the flesh of the melon along the seed line with a paring knife.  Now, lift off the piece you just cut out.
 

Using a fork, scrape the seeds from the piece you just removed and from the remaining flesh on the rind.
 

For storage, cut the flesh into cubes, place in a covered container and refrigerate.  It should keep for 3-4 days.
 

Look the cantaloupe over.  You are looking for a firm, symmetrical cantaloupe that is free from bruises, cuts or dents. 
 

The skin should be straw colored (not green) with a grey toned well defined netting.  If the skin is mottled straw-green color, it will ripen sitting out on a counter after a day or two and will be just as sweet as a fully ripe one.
 

Lift it up.  It should be heavy for its size and slightly soft at the blossom end.  (It should give slightly with mild pressure.  Don't puncture it.)
 

The cantaloupe should be aromatic.  You can sniff at the stem end if the stem is loose or detached.
 

Shake it!  If you can hear water inside reject it and select another.  Its flavor has been diluted by over-watering or it may have been dropped.