Artificial Intelligence (AI) methods, particularly Deep Neural Networks (DNNs), have shown great promise in a range of medical imaging tasks. However, the susceptibility of DNNs to producing erroneous outputs under the presence of input noise and variations is of great concern and one of the largest challenges to their adoption in medical settings. Towards addressing this challenge, we explore the robustness of DNNs trained for chest radiograph classification under a range of perturbations reflective of clinical settings. We propose RoMIA, a framework for the creation of Robust Medical Imaging AI models. RoMIA adds three key steps to the model training and deployment flow: (i) Noise-added training, wherein a part of the training data is synthetically transformed to represent common noise sources, (ii) Fine-tuning with input mixing, in which the model is refined with inputs formed by mixing data from the original training set with a small number of images from a different source, and (iii) DCT-based denoising, which removes a fraction of high-frequency components of each image before applying the model to classify it. We applied RoMIA to create six different robust models for classifying chest radiographs using the CheXpert dataset. We evaluated the models on the CheXphoto dataset, which consists of naturally and synthetically perturbed images intended to evaluate robustness. Models produced by RoMIA show 3%–5% improvement in robust accuracy, which corresponds to an average reduction of 22.6% in misclassifications. These results suggest that RoMIA can be a useful step towards enabling the adoption of AI models in medical imaging applications.