In many applications involving electromagnetic as well as optical waves, it is desirable to design materials that will have prescribed reflection and transmission characteristics as a function of frequency (narrow or wide band) and at the same time conform to restrictions on weight, structural properties, thickness, etc. Composite materials that contain a distribution of inclusions of specific concentration, distribution, geometry and material properties can often achieve such goals. Since the actual response of electronic and optical composite materials to the incident wave of low GHz to infrared frequency is quite diverse, it becomes very expensive and time consuming to actually prepare samples of such materials and test them experimentally. However, an optimal design through theoretical analysis of such materials is relatively efficient and the parameters involved are tractable. In this study, the damping characteristics of composites consisting of ferrite or chiral polymer inclusions embedded in a polymer matrix is examined. The reflection and transmission characteristics for a layer of such materials in response to incident millimeter-waves and microwaves will be presented with and without a conducting plate as a substrate.