Biopolymer-based blends of solid electrolytes capable of conducting sodium ions were prepared via solution casting by incorporating sodium carboxymethyl cellulose (NaCMC) and polyvinyl alcohol (PVA) with varying concentrations of sodium perchlorate monohydrate (NaClO4.H2O), which was used as the dopant. The prepared electrolytes were characterized to reveal their structural, vibrational, electrical, and electrochemical properties that make them promising as solid polymer electrolytes (SPEs). X-ray diffraction (XRD) analysis showed that the amorphous nature of the sample increased with the addition of NaClO4.H2O salt concentrations of up to 30 wt.%. The complexation between the polymers and salt was confirmed by Fourier-Transform Infrared (FTIR) analysis. The SPE exhibited an optimal ionic conductivity of (1.90 ± 0.05) ×10−5 S cm−1, which is three orders higher than that of the pristine polymer blend with (5.31 ± 0.61) ×10−8 S cm−1, as determined by electrochemical impedance spectroscopy (EIS) analysis. Scaling studies conducted based on AC conductivity and tangent loss revealed that these measurements could be represented by a single master curve, which suggests that the optimal sample adheres to the time-temperature superposition principle (TTSP). The temperature dependence of Jonscher's exponent indicates that the conduction mechanism can be effectively represented by the Quantum Mechanical Tunneling model (QMT). Both transference number measurement (TNM) and linear sweep voltammetry (LSV) analyses validated the electrolyte's suitability for energy device applications by demonstrating its high ion transference number and electrochemical potential window of 3.93 V. The optimized SPE film was subsequently utilized in an electrochemical double-layer capacitor (EDLC) device to evaluate its performance as both an electrolyte and separator. The supercapacitor exhibited an impressive energy density of 15.18 Wh kg−1 and a power density of 4512.5 W kg−1, along with remarkable stability in terms of cycle life.