As a type of figurative language, an East Asian idiom condenses rich cultural background into only a few characters. Translating such idioms is challenging for human translators, who often resort to choosing a context-aware translation from an existing list of candidates. However, compiling a dictionary of candidate translations demands much time and creativity even for expert translators. To alleviate such burden, we evaluate if GPT-4 can help generate high-quality translations. Based on automatic evaluations of faithfulness and creativity, we first identify Pareto-optimal prompting strategies that can outperform translation engines from Google and DeepL. Then, at a low cost, our context-aware translations can achieve far more high-quality translations per idiom than the human baseline. We open-source all code and data to facilitate further research.