The goal of extrinsic calibration is the alignment of sensor data to ensure an accurate representation of the surroundings and enable sensor fusion applications. From a safety perspective, sensor calibration is a key enabler of autonomous driving. In the current state of the art, a trend from target-based offline calibration towards targetless online calibration can be observed. However, online calibration is subject to strict real-time and resource constraints which are not met by state-of-the-art methods. This is mainly due to the high number of parameters to estimate, the reliance on geometric features, or the dependence on specific vehicle maneuvers. To meet these requirements and ensure the vehicle's safety at any time, we propose a miscalibration detection framework that shifts the focus from the direct regression of calibration parameters to a binary classification of the calibration state, i.e., calibrated or miscalibrated. Therefore, we propose a contrastive learning approach that compares embedded features in a latent space to classify the calibration state of two different sensor modalities. Moreover, we provide a comprehensive analysis of the feature embeddings and challenging calibration errors that highlight the performance of our approach. As a result, our method outperforms the current state-of-the-art in terms of detection performance, inference time, and resource demand. The code is open source and available on https://github.com/TUMFTM/MiscalibrationDetection.