It is known that slabs of wire media — dense arrays of thin conducting wires — can transport electromagnetic energy of evanescent plane waves over the slab thickness. This phenomenon was successfully used in superlenses and endoscopes. However, in the known configurations the effective energy transfer takes place only at the Fabry-Perot (thickness) resonances of the slab, making broadband power transfer impossible. In this paper we experimentally demonstrate that power transfer by a wire medium slab can be very broadband, whereas the Fabry-Perot resonances are damped, provided that the wires of the wire medium slab extend into the power-emitting body. As a testbed system we have used two rectangular waveguides and demonstrated that a properly designed and positioned wire medium slab transfers modes of any polarization from the input to the output waveguides. This study is relevant to emerging applications where broadband transport of reactive-field energy is required, especially in enhancing and controlling radiative heat flows in thermophotovoltaic systems.