Reliable evaluation of AI systems remains a fundamental challenge when ground truth labels are unavailable, particularly for systems generating natural language outputs like AI chat and agent systems. Many of these AI agents and systems focus on entity-centric tasks. In enterprise contexts, organizations deploy AI systems for entity linking, data integration, and information retrieval where verification against gold standards is often infeasible due to proprietary data constraints. Academic deployments face similar challenges when evaluating AI systems on specialized datasets with ambiguous criteria. Conventional evaluation frameworks, rooted in supervised learning paradigms, fail in such scenarios where single correct answers cannot be defined. We introduce VB-Score, a variance-bounded evaluation framework for entity-centric AI systems that operates without ground truth by jointly measuring effectiveness and robustness. Given system inputs, VB-Score enumerates plausible interpretations through constraint relaxation and Monte Carlo sampling, assigning probabilities that reflect their likelihood. It then evaluates system outputs by their expected success across interpretations, penalized by variance to assess robustness of the system. We provide formal theoretical analysis establishing key properties including range, monotonicity, and stability along with concentration bounds for Monte Carlo estimation. Through case studies on AI systems with ambiguous inputs, we demonstrate that VB-Score reveals robustness differences hidden by conventional evaluation frameworks, offering a principled measurement framework for assessing AI system reliability in label-scarce domains.