Polymer composites with electrically conductive inclusions are intensively developed for microwave shielding applications, where lightweight and elastic coatings are necessary. In this paper, dielectric properties of hybrid polyethylene composites containing cobalt nanoparticles and multi-wall carbon nanotubes (MWCNT) were investigated in the wide frequency range of 20 Hz–40 GHz for electromagnetic shielding applications. The percolation threshold in the hybrid system is close to 6.95 wt% MWCNT and 0.56 Co wt%. Cobalt nanoparticles (up to highest investigated concentration 4.8 wt%) had no impact on the percolation threshold, and for the fixed total concentration of fillers, the complex dielectric permittivity is higher for composites with bigger MWCNT concentrations. Moreover, the microwave complex dielectric permittivity of composites with high concentration of fillers is quite high (for composites with 13.4 wt% MWCNT and 1.1 wt% Co ε′ ≈ ε″ ≈ 20 at 30 GHz, it corresponds to microwave absorption 50% of 1 mm thickness plate); therefore, these composites are suitable for electromagnetic shielding applications.