High-quality guided wave devices are key components in integrated millimeter-wave circuits. In this paper, we propose mm-wave planar dielectric waveguides based on thin, anisotropic artificial dielectric layers with very high in-plane permittivity. Waves propagating on such films are surface waves whose field exponentially decays outside the film in the vertical direction, similar to waveguides commonly used in integrated optics. The very high in-plane permittivity of the artificial dielectric layers leads to strong field confinement, and allows the implementation of relatively thin waveguides. This fact, together with the planar structure of these devices, make them highly suitable for monolithic integration. Although the performance of the waveguide proposed is somewhat limited by effective electric and, in particular, magnetic polarization losses at mm-wave frequencies, extensive numerical calculations demonstrate the feasibility of devices with a quality factor up to 26 in the 55-90 GHz range on a 10 Ω.cm silicon substrate.Index Terms-planar waveguide; artificial dielectric; in-plane permittivity; perpendicular permeability, polarization loss