Another pic

You said you mixed old soil with new. Won't that have damaged roots some? They need some shade for a week or so until they get rooted. Several layers of the floating row cover should work.

Where had the seedlings been before you planted them out in a container? If you didn't harden them off correctly, they're probably undergoing some transplant shock. It looks (though I can't tell for certain because of the blurry photo) that they've got a bit of a sunburn. As fruitnut suggested, shade covers would be helpful.

Also, with the very hot sun, plants are naturally going to droop a little bit by evening. Look again tomorrow and see if the cool night air and the moisture has perked it up any. If it has, there's probably hope as long as you keep it shaded till it's acclimatized outside.

Thank you for the responses - I should have been more specific! First and foremost, these are the Sugar Baby variety (not sure if that matters?)

I transplanted them from a 12" round container to 2 10 gallon containers. The 12" was sort of a temporary home while I got my act together with the larger containers. They were very happy in the 12"....obviously not so much in the big containers. That's where the "extra" soil came from.

Plant #2 has perked back up, though one of the "vine" leaves is still wilted around the edges. Plant #1 is limp and leaning over. I will keep watch and see if there's any recovery. Is transplant shock something from which watermelons can come back?