Ok, thought since a few people had put their two cents in on this I thought I would as well, especially since shin splints seem to be a pretty common thing among traceurs.
One of the biggest thing with shin splints that can help to train the muscles surrounding the foot and ankle is unstable surface training. You don't need any weights, just some thick pillows or the cushions off of your couch. When standing on them if you perform squats, lunges, single leg squats, bicep curls (more or less any standing exercises) you force the muscles around the ankle, knee, hip, and core to activate for stability. This allows for improved strength and reaction time of those muscles without causing the stress of running or jumping. If you are really looking for a challenge do it with your eyes closed (be careful please). Additionally, it will work on your balance for precision jumps and improve proprioception (body/ joint position awareness), which is one of the 3 primary ways that you maintain balance (inner ear and vision being the other two).
If you are looking to train your tolerance of jumping without causing a lot of aggravation I would try jumping rope. Its still impact activity and if it causes pain you should stop, but it would allow for low intensity, endurance training for the muscles that are typically the cause of shin splints.
Hope this information is helpful.