I suffered with really bad shin splints at the start of the season and came upon some tips to getting rid of them (and still refereeing!)
purchase some calf guard compression (do a search on amazon). I wear them during the game (or any other running based exercise), during the shower post match and leave them on for a couple of hours afterwards. I paid £15 for the pair and they have lasted all season and are still in good shape. As an unexpected bonus I tuck the top of the sock into them and it holds the sock perfectly in place.
secondly, I found an exercise to build strength around the shin. Basically (1) walk on your tip toes (well on front pads of foot) for around 30 steps (2) without stopping switch to walking on the ball of your heel for another 30. Keep switching back and forth. I was just doing it whenever the chance arose, doing it everyday. Also added it to my prematch warm up in the changing room.
since starting the above the shin splints are gone. Aplogies for reviving an old thread but I hated having shin splints and though this might be of use.