I had been wondering the same thing. I have recently discovered Nikon's own screen protector for the D4 (they also make them for other models), which has their product code LP-SD4. These were £16.99 (inc. VAT) from the online Nikon (Europe) Store.
This is a hard protective film to protect from scratches. It has a non-reflective blue coating which they comment is non-reflective high-brightness reducing reflections from the monitor and providing a more precise hue and contrast. Consists of three custom cut films (one for each LCD) and there is a spare of each in the package.
They were very easy to apply (no bubbles) and came with a lint free cloth to clean the screens first. So far so good. In my opinion these would not protect from a really strong impact but should be a very useful first line of defence. They fit slightly inside boundary of the screen and visibility is good.
I'm pleased to have them in place and was pleased to use something that was actually made by Nikon, rather than a third party - especially given the value of the camera.