Computer-aided analytical studies and physical understanding of important characteristics of some commonly used left-handed material (LHM) structures (wire-array and split-ring resonator), to realize negative effective permittivity and permeability leading to negative refractive index over a desired frequency band have been reported in this paper. The transmission of electromagnetic wave through LHMs and right-handed materials (RHMs) has some fundamental differences. This issue of electromagnetic wave transmission through LHM has been characterized, and a physical insight of the phenomena has also been included. The LHM characterization using computer-aided analytical modeling shows good agreement with the previous numerical simulation and experimental results reported for such microstructures operating at microwave frequencies. © 2009 by the IETE.