This paper analyses the effectiveness of neural machine translation when applied to literary translation and, more specifically, to the translation of collocations, one of the most difficult aspects in machine translation (Corpas-Pastor 2015; Shraiden and Mahadin 2015). Literary translation continues to constitute one of the biggest challenges for machine translation (Toral and Way 2018), where cohesion errors are amongst the most frequent (Voigt and Jurafsky 2012). A comparative analysis of the translation of the first chapter of the world literature masterpiece El ingenioso hidalgo don Quijote de la Mancha — known as Don Quixote in English — was carried out, paying close attention to collocations. The human translation done by Tom Lathrop (Don Quixote) was compared to the target texts obtained with the two biggest neural machine translation systems today, Google Translate and DeepL, to see which provided more accurate results. The results confirm that neural machine translation offers highly reliable results. On a quantitative level the margins are very narrow when determining which system, DeepL or Google Translate, is better. DeepL scored better in terms of accuracy and recall, but in the BLEU metrics Google Translate scored 28.10 and DeepL 26.63. On a qualitative level and from a subjective point of view, the authors found DeepL’s translation to be somewhat more fluid and natural than Google Translate’s.