Machine unlearning provides viable solutions to revoke the effect of certain training data on pre-trained model parameters. Existing approaches provide unlearning recipes for classification and generative models. However, a category of important machine learning models, i.e., contrastive learning (CL) methods, is overlooked.In this paper, we fill this gap by first proposing the framework of Machine Unlearning for Contrastive learning (MUC) and adapting existing methods. Furthermore, we observe that several methods are mediocre unlearners and existing auditing tools may not be sufficient for data owners to validate the unlearning effects in contrastive learning. We thus propose a novel method called Alignment Calibration (AC) by explicitly considering the properties of contrastive learning and optimizing towards novel auditing metrics to easily verify unlearning. We empirically compare AC with baseline methods on SimCLR, MoCo and CLIP. We observe that AC addresses drawbacks of existing methods: (1) achieving state-of-the-art performance and approximating exact unlearning (retraining); (2) allowing data owners to clearly visualize the effect caused by unlearning through black-box auditing.