Artificial intelligence and machine learning are increasingly used for forecasting, optimization, and policy design in the energy sector, yet no standardized framework exists to evaluate whether these systems reason correctly. Current validation practices focus on predictive accuracy or computational efficiency, leaving the logical integrity of analytical conclusions untested. This study introduces the Analytical Reliability Benchmark (ARB), a reproducible framework that quantifies reasoning reliability in large language models applied to energy system analysis. The benchmark integrates five submetrics: accuracy, reasoning reliability, uncertainty discipline, policy consistency, and transparency, and evaluates model performance across deterministic, probabilistic, and epistemic scenarios using open technoeconomic datasets (NREL ATB 2024, DOE H2A/H2New, IEA WEO 2024). Four frontier models (GPT-4/5, Claude 4.5 Sonnet, Gemini 2.5 Pro, Llama 3 70B) were tested under identical factual and regulatory conditions. Results show that reasoning reliability can be objectively measured. GPT-4/5 and Claude 4.5 Sonnet achieved consistent and policy-compliant reasoning (Analytical Reliability Index greater than 90), Gemini 2.5 Pro demonstrated moderate stability, and Llama 3 70B remained below professional thresholds. Statistical validation confirmed that these differences are significant and reproducible. The ARB establishes the first quantitative method in the energy literature for verifying causal, probabilistic, and policy-driven reasoning in artificial intelligence systems, providing a reference framework for trustworthy and transparent analytical applications in the global energy transition.