Machine learning components such as deep neural networks are used extensively in cyber-physical systems (CPS). However, such components may introduce new types of hazards that can have disastrous consequences and need to be addressed for engineering trustworthy systems. Although deep neural networks offer advanced capabilities, they must be complemented by engineering methods and practices that allow effective integration in CPS. In this paper, we proposed an approach for assurance monitoring of learning-enabled CPS based on the conformal prediction framework. In order to allow real-time assurance monitoring, the approach employs distance learning to transform high-dimensional inputs into lower size embedding representations. By leveraging conformal prediction, the approach provides well-calibrated confidence and ensures a bounded small error rate while limiting the number of inputs for which an accurate prediction cannot be made. We demonstrate the approach using three datasets of mobile robot following a wall, speaker recognition, and traffic sign recognition. The experimental results demonstrate that the error rates are well-calibrated while the number of alarms is very small. Furthermore, the method is computationally efficient and allows real-time assurance monitoring of CPS.