In this work, we theoretically analyze the limitations for TM surface wave attenuation on lossy coated conducting surfaces containing electric and/or magnetic loss. We use both an analytical approach as well as numerical simulations, and find excellent agreement between them. We also find that the loss can be described by a simple approximate expression for a wide range of material properties. Furthermore, we analyze lossy slabs with simple equivalent circuit boundaries on top, such as may be provided by frequency selective surfaces or other patterned structures. We find that such composite lossy coating can exceed the attenuation of a simple lossy slab, but with limited bandwidth. We also find that only by increasing permeability, and not permittivity, can the peak absorption frequency be lowered for a given thickness without reducing the relative absorption bandwidth. © 2013 IEEE.