While machine translation systems have been applied to many tasks with remarkable success, machine poetry translation has remained a challenge. This study investigates the capabilities of generative Large Language Models (LLMs) in the translation of poetry (taking Shakespeare’s 154 sonnets as an example) from English to German. For this purpose, I define metrics that assess the reproduction of the rhyme scheme and the metre of the original in a quantitative way. The results indicate that LLMs still lag behind professional human translators (especially with regard to the reproduction of the rhyme scheme), but that their performance is significantly influenced by the chosen prompt strategy. In particular, iteratively refining the result emerges as a successful strategy in terms of the reproduction of the form, but this comes at the expense of other aspects such as grammaticality and the reproduction of the meaning.