Endoscopic systems and methods that provide wireless power transmission from a camera head to at least one solid-state light source housed in an endoscopic device. The endoscopic systems and methods employ a multi-stage electromagnetic induction coupling mechanism that can wirelessly transfer power from the camera head to an endocoupler, as well as from the endocoupler to the solid-state light source, while allowing axial rotational motion of at least the camera head, the endocoupler, and/or the endoscopic device relative to one another.