In-Context Learning (ICL) has become a standard technique for adapting Large Language Models (LLMs) to specialized tasks by supplying task-specific exemplars within the prompt. However, when these exemplars contain sensitive information, reliable privacy-preserving mechanisms are essential to prevent unintended leakage through model outputs. Many privacy-preserving methods have been proposed to protect against information leakage in this context, but there are fewer efforts on how to audit these methods. We introduce ContextLeak, the first framework to empirically measure the worst-case information leakage in ICL. ContextLeak uses canary insertion, embedding uniquely identifiable tokens in the sensitive dataset and crafting targeted queries to detect their presence. We apply ContextLeak across a range of private ICL techniques, including both heuristic prompt-based defenses and differentially private methods with formal guarantees. We show that ContextLeak reliably detects leakage across methods, and the leakage increases monotonically with the theoretical privacy budget, offering a practical signal of worst-case privacy risk. Our analysis further reveals that existing methods strike poor privacy-utility trade-offs, either completely leaking sensitive information or severely degrading performance.