Large language models (LLMs) have shown strong capabilities, enabling concise, context-aware answers in question answering (QA) tasks. The lack of transparency in complex LLMs has inspired extensive research aimed at developing methods to explain large language behaviors. Among existing explanation methods, natural language explanations stand out due to their ability to explain LLMs in a self-explanatory manner and enable the understanding of model behaviors even when the models are closed-source. However, despite these promising advancements, there is no existing work studying how to provide valid uncertainty guarantees for these generated natural language explanations. Such uncertainty quantification is critical in understanding the confidence behind these explanations. Notably, generating valid uncertainty estimates for natural language explanations is particularly challenging due to the auto-regressive generation process of LLMs and the presence of noise in medical inquiries. To bridge this gap, in this work, we first propose a novel uncertainty estimation framework for these generated natural language explanations, which provides valid uncertainty guarantees in a post-hoc and model-agnostic manner. Additionally, we also design a novel robust uncertainty estimation method that maintains valid uncertainty guarantees even under noise. Extensive experiments on QA tasks demonstrate the desired performance of our methods.