Recent advances in large language models (LLMs) have shown they can match or surpass finetuned models on many natural language processing tasks. Currently, more studies are being carried out to assess whether this performance carries over across different languages. In this paper, we present a thorough evaluation of LLMs for the less well-researched code-switching translation setting, where inputs include a mixture of different languages. We benchmark the performance of six state-of-the-art LLMs across seven datasets, with GPT-4 and GPT-3.5 displaying strong ability relative to supervised translation models and commercial engines. GPT-4 was also found to be particularly robust against different code-switching conditions. Several methods to further improve code-switching translation are proposed including leveraging in-context learning and pivot translation. Through our code-switching experiments, we argue that LLMs show promising ability for cross-lingual understanding.