A class of microcellular polymer nanocomposites of multi-walled carbon nanotubes (MWCNT) is reported that exhibits a stable and significantly high dielectric permittivity coupled with a stable and low dielectric loss in a wide range of frequency. Polypropylene (PP)-MWCNT nanocomposites with a cellular structure were prepared by melt mixing followed by physical foaming in an injection molding process. The generation of a cellular structure inside the nanocomposites provides a unique planar-like arrangement of the MWCNTs around the cells. This enhances the dielectric permittivity of nanocomposites up to an order of magnitude. Therefore, microcellular PP-1.25 vol% MWCNT presents a dielectric permittivity of ε′=57.2 and a dielectric loss of tan δ=0.05 at 0.1 MHz, highly superior to the best values of the solid nanocomposites prepared by regular compression molding (ε′=14.1 and tan δ=0.39) and by injection molding (ε′=17.8 and tan δ=0.04). Also, microcellular PP-1.66 vol% MWCNT exhibits ε′=95.6 and tan δ=0.14, which surpasses the dielectric performances reported in the literature. Hence, these nanocomposites with a cellular structure provide a novel and general approach to develop microscopically tailored structures for dielectric applications using facile methods. Such dielectrics can be used for energy storage in modern electronics and electrical power systems.