The rare-earth-doped zirconia-based solid electrolytes have gained significant interest in protonic ceramic fuel cell (PCFC) applications due to their high ionic conductivity. However, these solid electrolytes are susceptible to low conductivity and chemical stability at low operating temperatures, which are of interest in commercializing ceramic fuel cells. Thus, tailoring the structural properties of these electrolytes towards gaining high ionic conductivity at low/intermediate temperatures is crucial. In this study, Ce (cerium) and Nd (neodymium) co-doped barium zirconate perovskites, BaZr(0.80-x-y)CexNdyY0.10Yb0.10O3-δ (BZCNYYO) of various doping fractions (x, y: 0, 0.5, 0.10, 0.15), were synthesized (by the Pechini method) to systematically analyze their structural and conductivity properties. The X-ray diffraction patterns showed a significant lattice strain, and the stress inferences for each co-doped BZCNYYO sample were compared with Nd-cation-free reference samples, BaZrO3 and BaZr(0.80-x-y-z)CexYyYbzO3-δ (x: 0, 0.70; y: 0.20, 0.10; z: 0, 0.10). The comparative impedance investigation at low-to-intermediate temperatures (300–700 °C) showed that BaZr0.50Ce0.15Nd0.15Y0.10Yb0.10O3-δ offers the highest lattice strain and stress characteristics with an ionic conductivity (σ) of 0.381 mScm−1 at 500 °C and activation energy (Ea) of 0.47 eV. In addition, this σ value was comparable to the best reference sample BaZr0.10Ce0.70Y0.10Yb0.10O3-δ (0.404 mScm−1) at 500 °C, and it outperformed all the reference samples when the set temperature condition was ≥600 °C. The result of this study suggests that Ce- and Nd-doped BZCNYYO solid electrolytes will be a specific choice of interest for developing intermediate-temperature PCFC applications with high ionic conductivity.