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Carbon nanostructures such as carbon nanotubes and most recently discovered graphenes can be included in very low weight percentages in a polymer matrix to create new lightweight nanocomposites with improved electrical, electromagnetic and mechanical performances. The present study shows the effect of the filler type and concentration, and of the characteristics of the thermosetting resin, on both the effective complex permittivity and the effective conductivity of the nanocomposites at radio-frequency. Three different types of fillers are considered: commercially available multi-wall carbon nanotubes and nickel-coated microfibers, and graphene nanoplatelets produced in our lab. The results show that it is possible to produce nanocomposites with tailored electromagnetic properties, i.e. with controlled dielectric constant and effective conductivity at the same time, by properly selecting the type of matrix used, considering the characteristics of the nanofiller.