A frequency-domain (FD) uniform asymptotic solution (FD-UAS) which is useful for engineering applications is newly derived for the two-dimensional scattered magnetic field by a coated conducting cylinder covered with a thin lossy medium. The FD-UAS is uniform in the sense that it remains valid within the transition region adjacent to the shadow boundary, and it smoothly connects a geometric optical ray (GO) solution and a geometrical theory of diffraction (GTD) solution exterior to the transition region, respectively. We assume that the thickness of a coating medium is thin as compared with one wavelength of a cylindrical wave radiated from a magnetic line source. This uniform asymptotic solution is represented by a combination of scattered field component solutions, namely, the GO solution composed of a direct GO (DGO) and a reflected GO, the extended uniform GTD (extended UTD) solution made up of a DGO and a pseudo surface diffracted ray (pseudo SD), the modified UTD solution representing SD series, and the GTD solution for a lowest order SD. The FD-UAS is valid for a source point and/or an observation point located either near the coating surface or in the far-zone. The effectiveness and usefulness of the FD-UAS presented here are confirmed by comparing with both the exact solution and the conventional UTD shadow region solution.