I've been surprised how difficult it is for LLMs to simply answer "I don't know."
It also seems oddly difficult for them to 'right-size' the length and depth of their answers based on prior context. I either have to give it a fixed length limit or put up with exhaustive answers.
The best pro/research-grade models from Google and OpenAI now have little difficulty recognizing when they don't know how or can't find enough information to solve a given problem. The free chatbot models rarely will, though.