Users have become increasingly reliant on Large Language Models (LLMs) to complete a wide range of reasoning tasks, from managing workplace projects to giving personal advice. However, LLMs function as black boxes, leaving users with minimal insight into how they generate the responses that they do. One way that users can attempt to peek into these black boxes is by asking LLMs to explain their reasoning processes. The nascent literature on LLM faithfulness suggests that LLMs – like humans – often fail to accurately identify the information they use to inform their reasoning, suggesting a lack of metacognitive knowledge. We extend this research to the context of value-based, multi-attribute choice, tasking both LLMs and human participants (n = 436) with completing the Knowledge of Weights paradigm. Participants first completed a series of choice tasks in which they picked between homes that varied on six attributes, then self-reported the decision weight they believed they had placed on each attribute in two different formats. We found that ChatGPT4o, the oldest model tested, self-reported weights that were significantly less reflective of its choice behavior than humans. However, three newer, more-advanced LLMs (ChatGPT5, Sonnet 4, and Gemini 2.5 Flash) self-reported weights that were as accurate or more accurate than those provided by humans. These results suggest that LLMs can generate and maintain accurate metacognitive knowledge of their own decision-making processes as well or better than humans, but that this is a relatively new ability. Practical and theoretical implications are discussed.