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In this study the authors present a new surface-impedance model for the accurate computation of the effect of metal losses on the parameters of printed microstrip lines. The novelty of the authors' approach lies in the fast and direct calculation of the tangential magnetic fields above and below the strip conductors, which allows us to develop a very efficient quasi-transverse electromagnetic (TEM) solution for the conductor losses of multilayer single or coupled microstrip lines. The overall computational effort of the authors' method is much less than that required by purely numerical approaches. The accuracy of the method has been verified by comparison with other techniques, including a general-purpose full-wave finite elements method. It is also shown that the proposed method provides better results than other previously surface-impedance approaches.