The extraction of interactions between chemicals and proteins from several biomedical articles is important in many fields of biomedical research such as drug development and prediction of drug side effects. Several natural language processing methods, including deep neural network (DNN) models, have been applied to address this problem. However, these methods were trained with hard-labeled data, which tend to become over-confident, leading to degradation of the model reliability. To estimate the data uncertainty and improve the reliability, "calibration" techniques have been applied to deep learning models. In this study, to extract chemical--protein interactions, we propose a DNN-based approach incorporating uncertainty information and calibration techniques. Our model first encodes the input sequence using a pre-trained language-understanding model, following which it is trained using two calibration methods: mixup training and addition of a confidence penalty loss. Finally, the model is re-trained with augmented data that are extracted using the estimated uncertainties. Our approach has achieved state-of-the-art performance with regard to the Biocreative VI ChemProt task, while preserving higher calibration abilities than those of previous approaches. Furthermore, our approach also presents the possibilities of using uncertainty estimation for performance improvement.