High-entropy ceramics (HECs) have attracted considerable attention for their potential in electromagnetic wave absorption because of their tunable composition and complex microstructures. However, the current challenges in this field include a limited understanding of the relationships among the composition, microstructure, and electromagnetic properties, as well as the difficulty in achieving a good balance between strong absorption intensity and broad bandwidth. To address these issues, (Hf_(1−X)/4Zr_(1−X)/4Nb_(1−X)/4Ta_(1−X)/4Co_X)C (X = 0.14, 0.18, and 0.20) high-entropy ceramic powders were successfully synthesized via a polymer-derived ceramic (PDC) method at 1700–1900 °C. Structural analysis confirmed the formation of single-phase rock‒salt structures with homogeneous elemental distributions and significant lattice distortion. The (Hf_0.215Zr_0.215Nb_0.215Ta_0.215Co_0.140)C ceramic prepared at 1700 °C exhibited excellent reflection loss (RL) of −37.95 dB at 14.01 GHz with a thickness of 3.10 mm. The introduction of the magnetic element cobalt optimized the permeability and dielectric constant of the sample, significantly enhancing the dielectric–magnetic loss synergy. This work bridges the gap in systematic research on incorporating Co into high-entropy carbide ceramics and provides new insights for designing high-performance electromagnetic wave absorbing materials.