Large Reasoning Models (LRMs) suffer from sycophantic behavior, where models tend to agree with users' incorrect beliefs and follow misinformation rather than maintain independent reasoning. This behavior undermines model reliability and poses societal risks. Mitigating LRM sycophancy requires monitoring how this sycophancy emerges during the reasoning trajectory; however, current methods mainly focus on judging based on final answers and correcting them, without understanding how sycophancy develops during reasoning processes. To address this limitation, we propose MONICA, a novel Monitor-guided Calibration framework that monitors and mitigates sycophancy during model inference at the level of reasoning steps, without requiring the model to finish generating its complete answer. MONICA integrates a sycophantic monitor that provides real-time monitoring of sycophantic drift scores during response generation with a calibrator that dynamically suppresses sycophantic behavior when scores exceed predefined thresholds. Extensive experiments across 12 datasets and 3 LRMs demonstrate that our method effectively reduces sycophantic behavior in both intermediate reasoning steps and final answers, yielding robust performance improvements.