Something I imagine might work (though not really as a shield, but more of a preventative measure) would be to have a few objects in orbit with a very large surface area, so that orbital debris is likely to run into it and get knocked into an orbit that intersects the atmosphere. Let's say these objects have a thousand times more surface area than the objects you actually care about. This would mean that any random piece of debris is far more likely to hit the large debris target than the important satellites.

Making something that can be hit by random objects at extreme velocities without generating even more debris sounds like a hard problem, though. Ice would be an interesting material because it sublimates, but it happens too quickly to be practically useful.