In this study, we examine the electrochemical performance of supercapacitor (SC) electrodes made from 3D-printed nanocomposites. These composites consist of multiwalled carbon nanotubes (MWCNTs) and polyether ether ketone (PEEK), coated with poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS). The electrochemical performance of a 3D-printed PEEK/MWCNT solid electrode with a surface area density of 1.2 mm is compared to two distinct periodically porous PEEK/MWCNT electrodes with surface area densities of 7.3 and 7.1 mm. To enhance SC performance, the 3D-printed electrodes are coated with a conductive polymer, PEDOT:PSS. The architected cellular electrodes exhibit significantly improved capacitive properties, with the cellular electrode (7.1 mm) displaying a capacitance nearly four times greater than that of the solid 3D-printed electrode-based SCs. Moreover, the PEDOT:PSS-coated cellular electrode (7.1 mm) demonstrates a high specific capacitance of 12.55 mF·cm at 50 mV·s, contrasting to SCs based on 3D-printed cellular electrodes (4.09 mF·cm at 50 mV·s) without the coating. The conductive PEDOT:PSS coating proves effective in reducing surface resistance, resulting in a decreased voltage drop during the SCs' charging and discharging processes. Ultimately, the 3D-printed cellular nanocomposite electrode with the conductive polymer coating achieves an energy density of 1.98 μW h·cm at a current of 70 μA. This study underscores how the combined effect of the surface area density of porous electrodes enabled by 3D printing, along with the conductivity imparted by the polymer coating, synergistically improves the energy storage performance.