This paper from ICRA 2008 details the construction of a 60cm x 60 cm surface that provides wireless (battery-free) power and bidirectional communication to an initial swarm consisting of five line-following robots, each consuming 200 mW. Power transmission in the system was achieved through magnetic flux coupling between a high Q L-C resonator placed beneath the operating surface and a non-resonant pickup coil on each robot. The average power density demonstrated was 4.1mW/cm2 for a static load, and the paper demonstrates much greater peak power for dynamic loads via capacitor storage and power conditioning circuitry.
See the paper (and related blog post) by Travis Deyle (myself) for additional details. The slides from the ICRA 2008 presentation are also available here. Finally, a video of the swarm operating battery-free on the surface is shown below. Also shown in the video is an LED being powered by the surface.