Machine translation (MT) models are known to suffer from gender bias, especially when translating into languages with extensive gendered morphology. Accordingly, they still fall short in using gender-inclusive language, also representative of non-binary identities. In this paper, we look at gender-inclusive neomorphemes, neologistic elements that avoid binary gender markings as an approach towards fairer MT. In this direction, we explore prompting techniques with large language models (LLMs) to translate from English into Italian using neomorphemes. So far, this area has been under-explored due to its novelty and the lack of publicly available evaluation resources. We fill this gap by releasing Neo-GATE, a resource designed to evaluate gender-inclusive en-it translation with neomorphemes. With Neo-GATE, we assess four LLMs of different families and sizes and different prompt formats, identifying strengths and weaknesses of each on this novel task for MT.