Despite the recent ubiquity of large language models and their high zero-shot prompted performance across a wide range of tasks, it is still not known how well they perform on tasks which require processing of potentially idiomatic language. In particular, how well do such models perform in comparison to encoder-only models fine-tuned specifically for idiomaticity tasks? In this work, we attempt to answer this question by looking at the performance of a range of LLMs (both local and software-as-a-service models) on three idiomaticity datasets: SemEval 2022 Task 2a, FLUTE, and MAGPIE. Overall, we find that whilst these models do give competitive performance, they do not match the results of fine-tuned task-specific models, even at the largest scales (e.g. for GPT-4). Nevertheless, we do see consistent performance improvements across model scale. Additionally, we investigate prompting approaches to improve performance, and discuss the practicalities of using LLMs for these tasks.