With an increasing number of parameters and pre-training data, generative large language models (LLMs) have shown remarkable capabilities to solve tasks with minimal or no task-related examples. Notably, LLMs have been successfully employed as evaluation metrics in text generation tasks. Within this context, we introduce the Eval4NLP 2023 shared task that asks participants to explore prompting and score extraction for machine translation (MT) and summarization evaluation. Specifically, we propose a novel competition setting in which we select a list of allowed LLMs and disallow fine-tuning to ensure a focus on prompting. We present an overview of participants' approaches and evaluate them on a new reference-free test set spanning three language pairs for MT and a summarization dataset. Notably, despite the task's restrictions, the best-performing systems achieve results on par with or even surpassing recent reference-free metrics developed using larger models, including GEMBA and Comet-Kiwi-XXL. Finally, as a separate track, we perform a small-scale human evaluation of the plausibility of explanations given by the LLMs.