Electrochemical capacitors (ECs) offer superior specific capacitance for energy storage compared to traditional electrolytic capacitors but face limitations in alternating current (AC) filtering due to the need for balancing fast response and high capacitance. This study addresses these challenges by developing a freestanding nanostructured carbon electrode, derived from the rapid carbonization of bacterial cellulose (BC) embedded with zeolitic imidazolate framework 8 (ZIF‐8) and in situ formed carbon nanotubes (CNTs). The electrode exhibits an exceptionally low area resistance of 9.8 mΩ cm2 and a high specific capacitance of 2.1 mF cm−2 at 120 Hz, maintaining performance even at high frequencies. Stacking these electrodes enhances the capacitance to 5.3 mF cm−2, with the phase angle degrading to −74.4° at 120 Hz; however, they retain a phase angle below −45° up to ≈50 kHz, demonstrating excellent high‐frequency performance. Furthermore, connecting three aqueous units in series as an integrated cell or utilizing organic electrolytes extends the voltage window to 2.4 V, enhancing their suitability for high‐voltage applications. Ripple voltage analysis under various loads and frequencies indicates effective filtering capabilities, highlighting the potential of these nanostructured ECs for next‐generation electronic applications.