The authors propose a theoretical model of coupling of ion Bernstein (IB) waves to tokamak plasma using phased waveguides. To describe the propagation of these waves near higher harmonics of the ion cyclotron frequency, a set of differential wave equations is used, constructed by analogy to the familiar finite Larmor radius wave equations, but in such a way that its three independent WKB solutions correspond to the two cold plasma waves and the Bernstein wave to all orders in the ion Larmor radius. This system has a meaningful energy theorem and unambiguous boundary conditions at the plasma edge. It is integrated numerically to obtain the surface admittance matrix of the plasma. The efficiency of waveguide launching is evaluated by extending the theory developed for lower hybrid wave grills to take into account the finite height of the waveguides as well as the coupling between TE and TM modes at the waveguide mouths due to the fact that at these frequencies the admittance matrix is not diagonal