Although machine learning (ML) and deep learning (DL) methods are increasingly used for anomaly detection in industrial cyber-physical systems, their adoption is hindered by concerns about model trustworthiness, especially high false alarm rates (FARs). Excessive false alarms overwhelm operators, cause unnecessary shutdowns, and reduce operational efficiency. This study addresses these challenges by proposing a novel framework that integrates ML-based anomaly detectors with conformal prediction (CP), a model-agnostic uncertainty quantification technique. To handle distribution shifts in time-series data, our framework incorporates a temporal quantile adjustment method with a sliding calibration set, ensuring statistical guarantees on predefined FARs. A rejection mechanism is further integrated by excluding significant anomalies from the calibration set, improving detection capability while maintaining FAR guarantees. For real-time anomaly monitoring, two P-value-based indicators generated from CP are developed to track anomalous trends and enhance model interpretability. The framework is evaluated by comparing several baseline ML and DL methods to their conformalized counterparts using a public ICPS dataset. Comparative results based on Precision, Recall, F1, and AUROC validate the framework’s compatibility with various ML models and its effectiveness in improving anomaly detection performance by reducing false alarms and guaranteeing FARs across a range of predefined values.