I won't remove anything from vines with fruit unless there is lots of vine and little fruit. Often cantaloupe overset and fruit quality suffers. Obviously if a plant has no fruit, it can be cut back or removed. When they get intertwined it's hard to tell what fruit goes with what plant.

The vines aren't doing nothing, they're nourishing your fruits.

Thank you fruitnut & ltilton. I appreciate the quick responses. I hope I'm using the correct nomenclature when I say vine because I don't understand how a 'vine' is nourishing fruit that is on another 'vine'. Should I be stating "branches" instead? As you can tell, I'm new to this.

Sometimes people call a melon plant a vine. But vine would be more correct as a name for one of the runners on a plant. The vines on one plant don't nourish fruit on another plant.

Any plant without fruit can be removed entirely or some of it's runners can be removed. But where you are there is still time to possibly set more fruit

If one runner/vine on a plant has fruit and another runner/vine on the same plant doesn't have fruit, both runners will feed the fruit. So keep all runners on any plant with fruit unless you are really cramped for space.

Thank you so much, fruitnut. Runner it is.
I have a watermelon and a cantaloupe in a 3' x 6' bed with the house as one boundary and the lawn as another. They are 3' apart and both on a single trellis that is 7' x 7'. The entire trellis is taken up and would like to make more room for the watermelon. As I said, the cantaloupe only has one runner with fruit and the other runners are making undersized male and few female flowers. If removing a runner would jeopardize the existing fruit on another, then case closed.