Tennis Elbow bands compress muscles in order to create less torque in your forearm so that your elbow does not have to absorb as much shock. They can also create heat around your elbow area while you are playing tennis to stimulate healing.
Of course, it is easier to play without a tennis elbow band and they can take some getting used to. They should keep the restriction of your range of motion and your circulation to a minimum and have good ventilation. There are various types of elbow bands, which you may need to use as you start your recovery, depending on the severity of your condition you may need to use one of the following types: elastic braces, hinged braces, magnetic braces, neoprene braces, sports & elbow pads or tennis and arm straps.
If you have followed the advice on this website regarding your tennis equipment, you will be able to eliminate or greatly reduce your need for any of these elbow bands. I have found a great resource for finding the best elbow bands is at The Brace Shop. See additional elbow bands.