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Skin cancer is the most common malignancy in the world. Automated skin cancer detection would significantly improve early detection rates and prevent deaths. To help with this aim, a number of datasets have been released which can be used to train Deep Learning systems - these have produced impressive results for classification. However, this only works for the classes they are trained on whilst they are incapable of identifying skin lesions from previously unseen classes, making them unconducive for clinical use. We could look to massively increase the datasets by including all possible skin lesions, though this would always leave out some classes. Instead, we evaluate Siamese Neural Networks (SNNs), which not only allows us to classify images of skin lesions, but also allow us to identify those images which are different from the trained classes - allowing us to determine that an image is not an example of our training classes. We evaluate SNNs on both dermoscopic and clinical images of skin lesions. We obtain top-1 classification accuracy levels of 74.33% and 85.61% on clinical and dermoscopic datasets, respectively. Although this is slightly lower than the state-of-the-art results, the SNN approach has the advantage that it can detect out-of-class examples. Our results highlight the potential of an SNN approach as well as pathways towards future clinical deployment., Comment: 10 pages, 5 figures, 5 tables