This may be of interest to you:
This article mentions that the only cable from the monitor would be for power. However there are new tests currently in place for wireless power. It works in very much the same way that a recharger for an electric tootbrush works. There is no direct connection to the power but works instead on an induction coil in the base.
Currently there is a possibility that soon we can have a coil fitted to a room which would power low demand devices such as mobile phones for charging. Whether or not this same technology can be applied to higher demand power devices (such as a monitor) is yet to be seen.