This paper proposes a robust system for detecting North Atlantic right whales by using deep learning methods to denoise noisy recordings. Passive acoustic recordings of right whale vocalisations are subject to noise contamination from many sources, such as shipping and offshore activities. When such data are applied to uncompensated classifiers, accuracy falls substantially. To build robustness into the detection process, two separate approaches that have proved successful for image denoising are considered. Specifically, a denoising convolutional neural network and a denoising autoencoder, each of which is applied to spectrogram representations of the noisy audio signal, are developed. Performance is improved further by matching the classifier training to include the vestigial signal that remains in clean estimates after the denoising process. Evaluations are performed first by adding white, tanker, trawler, and shot noises at signal-to-noise ratios from −10 to +5 dB to clean recordings to simulate noisy conditions. Experiments show that denoising gives substantial improvements to accuracy, particularly when using the vestigial-trained classifier. A final test applies the proposed methods to previously unseen noisy right whale recordings and finds that denoising is able to improve performance over the baseline clean-trained model in this new noise environment.