You describe a very common problem that lots of folks have with their horses, Pam. Because horses are herd animals, they often become nervous and uncomfortable when they lose sight of other horses. Here are two exercises you can use to help decrease or eliminate the behavior.
First, separate your horses during activities that they enjoy, like feeding time and grooming time. Keep these sessions short and fun. You are looking for them to begin to anticipate time without one another. Over time, you should observe them pacing the fence for you to come and separate them!
The second exercise is a bit harder to do and takes a bit more patience, but is well worth the effort. Your goal is to teach the horse you are riding that nickering and fretting will never result in going back to his pal, and that relaxing on the way home assures a quick reunion.
Ride off with one of your horses so that he is out of sight of his pal. Ideally, you will be in a ring or some other area big enough for large circles, but still within hearing range of the other horse. Ride as you would in this area, and when you are done with your ride, observe your horse’s behavior. If he is nickering or seeking his pal, circle away from the path toward home until the seeking stops. When it ceases (look for a relaxed head and neck, and low tail set), turn back toward the path. If he begins to seek again, turn and circle. Be sure to stay very calm and soft in voice and body. You are simply teaching him: nickering and fretting=no reunion; relaxing=reunion. You may be in for a long haul the first couple of days, but your horse will learn the game fairly quickly.