The effectiveness of equivalent transformation method of material constants (ETMMCs) is introduced through an example of the matching characteristics of a flat single-layer selective magnetic absorber (FSLSMA) with periodic conductive line frames (PCLFs). First, the matching characteristics of magnetic absorbers mounted on conductive line lattice, cross, square-frame, and double-layered PCLFs are simply introduced. Using finite-difference time-domain analysis and experimentations, the detailed matching characteristics focused on the FSLSMA with PCLFs are investigated. In particular, parametric investigations of the matching characteristics are conducted, which are related to the PCLF distributions, frame size, and material constants of the absorbers. Further, the present matching mechanisms and the design principles are clarified on the basis of the behavior of normalized input admittance in a Smith chart. The effectiveness of ETMMCs is demonstrated by designing a thin magnetic absorber with a thickness of 2 mm in the Industry, Science, and Medical frequency band of 2.45 GHz.