Structured Outputs from current LLMs exhibit sporadic errors, hindering enterprise AI deployment. We present CONSTRUCT, a real-time uncertainty estimator that scores the trustworthiness of LLM Structured Outputs. Lower-scoring outputs are more likely to contain errors, enabling automatic prioritization of limited human review bandwidth. CONSTRUCT additionally scores the trustworthiness of each field within a Structured Output, helping reviewers quickly identify which parts of the output are incorrect. Our method is suitable for any LLM (including black-box LLM APIs without logprobs), does not require labeled training data or custom model deployment, and supports complex Structured Outputs with heterogeneous fields and nested JSON schemas. We also introduce one of the first public LLM Structured Output benchmarks with reliable ground-truth values. Over this four-dataset benchmark, CONSTRUCT detects errors in outputs from various LLMs (including Gemini 3 and GPT-5) with significantly higher precision/recall than existing techniques.