As Bgrazman points out the cage does not need to be a solid sheet of conductive material. A wire mesh with quite wide wire spacing works fine. Indeed, your metal car provides good protection from lightning strikes even though it has large openings for windows.
Also, as Jea48 points out, grounding is not necessary, although it might be a good idea if only for safety reasons. When I installed shielded 300 ohm twinlead wire from a roodtop FM antenna I was surprised to find that the shield, for which I had paid extra $, was left unconnected at both ends. Seemed like a waste, but it worked great for eliminating interference from passing auto trafic.
Also, as Jea48 points out, grounding is not necessary, although it might be a good idea if only for safety reasons. When I installed shielded 300 ohm twinlead wire from a roodtop FM antenna I was surprised to find that the shield, for which I had paid extra $, was left unconnected at both ends. Seemed like a waste, but it worked great for eliminating interference from passing auto trafic.