Mitigating hallucination in large language models (LLMs) is crucial to ensure trustworthy generation. A meaningful solution to tackle this issue involves eliciting a reliable confidence score in the generation. However, the previous methods only focused on using white-box models for short-form generation. The solutions to long-form sentences with black-box models remain very limited. This study proposes a reliable black-box confidence elicitation for long-form generation by leveraging the external knowledge, inspired by retrieval augmented generation. In particular, this paper proposes the confidence-aware prompt refinement (CAPR) to modify user prompts to ensure trustworthy responses. The prompt refiner is trained by maximizing the rewards based on the confidence and the accuracy of generated sentences. Experiments show that CAPR effectively elicits reliable confidence scores. The refined prompts enable LLMs to produce reliable responses with calibrated confidence.