From y experience in EM labs they always use batteries as much as they can. High power for automotive inverters is fed in with heavy filter boxes, though they are mostly used only as a known characteristic for the measurement, since they will not block all RF.
As Ian.M said mechanical could be the way to go, though it also depends on your power and shielding demand. Grounding the mechanical feed through will only get you partway, it is very difficult to get a seal all around the shaft wile its spinning fast. If you want to go all the way you could use liquid metal sealed around the shaft. Another way could also be to use hydraulics, a pump and a motor, each with a generator/motor, getting the liquid shielded should be pretty easy with small enough pipe diameter and the transmittable power an be gigantic.
For ow power maybe optics? Laser through a mesh or a fiber lighting a solar cell.