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We report on a new principle yielding enhanced electromagnetic shielding, using as an example a composite comprised of carbon nanotubes (CNTs) integrated with a reactive ethylene terpolymer (RET). Such composites were synthesized through the chemical reaction of the functional groups on the CNT with the epoxy linkage of the RET polymer. The main advantages of these composites include good dispersion with low electrical percolation volume fractions (~0.1 volume%), yielding outstanding microwave shielding efficiency for electromagnetic interference applications. The shielding effectiveness was characterized for both single-walled and multiwalled CNT-based composites and was much enhanced in the former. The specific roles of absorption and reflection in determining the total shielding, as a function of the nanotube filling fraction, is also discussed.