This study addresses the critical challenge in solid-state batteries (SSBs) by analyzing sodium dendrite formation in Na5SmSi4O12 (NaSmSiO) solid electrolytes qualitatively and quantitatively. Symmetric Na|NaSmSiO|Na cells show negligible interfacial resistances and a high ionic conductivity of (1.5 ± 0.1) mS cm−1 at 30 °C with an activation energy for sodium transport of (0.31 ± 0.1) eV. Dendrite formation is systematically induced using a linear current ramp of 1 mA cm−2 h−1. Short circuits manifest as sharp resistance drops upon reaching the critical current density and are visually correlated with highly localized sodium filament penetration through the solid electrolyte. This observation indicates the presence of a “weakest link” within the material. The thermodynamics of this behavior are discussed. A statistical analysis of 30 cell tests reveals an average critical current density of 0.96 mA cm−2. Failure occurrence is fitted to a shifted Weibull distribution. The resulting shape parameter of 1.10 suggests an approximately consistent failure rate above a critical threshold of 0.47 mA cm−2. This work establishes quantitative benchmarks for NaSmSiO's dendrite resistance and introduces a robust statistical framework which can serve as a reference for future studies in this field.