In recent years, Transformers, initially developed for language, have been successfully applied to visual tasks. Vision Transformers have been shown to push the state-of-the-art in a wide range of tasks, including image classification, object detection, and semantic segmentation. While ample research has shown promising results in art attribution and art authentication tasks using Convolutional Neural Networks, this paper examines if the superiority of Vision Transformers extends to art authentication, improving, thus, the reliability of computer-based authentication of artworks. Using a carefully compiled dataset of authentic paintings by Vincent van Gogh and two contrast datasets, we compare the art authentication performances of Swin Transformers with those of EfficientNet. Using a standard contrast set containing imitations and proxies (works by painters with styles closely related to van Gogh), we find that EfficientNet achieves the best performance overall. With a contrast set that only consists of imitations, we find the Swin Transformer to be superior to EfficientNet by achieving an authentication accuracy of over 85%. These results lead us to conclude that Vision Transformers represent a strong and promising contender in art authentication, particularly in enhancing the computer-based ability to detect artistic imitations.