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For most of the electromagnetic applications, the materials can be defined in terms of their constitutive properties usually expressed in terms of their effective permittivity and permeability. The accurate knowledge of these properties is quite helpful in order to understand and analyze various concepts. These properties are also required for the effective usage of materials in various scientific and industrial areas. Recently, the knowledge of effective constitutive properties of artificial dielectrics such as composites and metamaterials has become quite important especially for the design of an efficient electromagnetic absorber using these materials. This work deals with the extraction of effective constitutive properties of artificial dielectrics including various composites and metamaterial structures using the short circuit waveguide method. The validation of the proposed approach has been carried out with the conventional transmission-reflection method for a number of standard materials. The proposed method has successfully been used for the extraction of the effective constitutive properties of a number of standard dielectrics as well as metamaterial structures.