As AI systems are increasingly used to draft radiology reports, reliably evaluating their clinical quality remains a critical challenge. Large language model (LLM)-based metrics are now the best-correlated with radiologist judgment, yet they output a single opaque score that neither a clinician nor a model builder can easily interpret or audit. We introduce RadMatch, a multi-stage, LLM-based metric that decomposes report comparison into a structured finding-level matching with significance-aware scoring and error characterization across seven clinical attribute dimensions (status, location, severity, morphology, certainty, longitudinal comparison, and measurement). The main score is the actionable-error count, both interpretable and auditable. Candidate findings are graded correct, partial, or incorrect, and unmatched findings are counted as missed or hallucinated. Triage and actionable safety recall/precision and per-subset views add complementary, deployment-oriented lenses. Across two expert benchmarks, RadMatch is the most clinically aligned metric, matching inter-radiologist agreement on ReXVal and more than doubling the best prior metric on the harder RadEvalExpert. Relying only on few-shot prompting, it is designed to extend to other modalities and anatomies. We will release RadMatch as open-source code with an interactive dashboard for inspecting results.

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