Large language models (LLMs) have demonstrated robust capabilities across various natural language tasks. However, producing outputs that are consistently honest and helpful remains an open challenge. To overcome this challenge, this paper tackles the problem through two complementary directions. It conducts a comprehensive benchmark evaluation of ten widely used large language models, including both proprietary and open-weight models from OpenAI, Meta, and Google. In parallel, it proposes a novel prompting strategy, self-critique-guided curiosity refinement prompting. The key idea behind this strategy is enabling models to self-critique and refine their responses without additional training. The proposed method extends the curiosity-driven prompting strategy by incorporating two lightweight in-context steps including self-critique step and refinement step. The experiment results on the HONESET dataset evaluated using the framework $\mathrm{H}^2$ (honesty and helpfulness), which was executed with GPT-4o as a judge of honesty and helpfulness, show consistent improvements across all models. The approach reduces the number of poor-quality responses, increases high-quality responses, and achieves relative gains in $\mathrm{H}^2$ scores ranging from 1.4% to 4.3% compared to curiosity-driven prompting across evaluated models. These results highlight the effectiveness of structured self-refinement as a scalable and training-free strategy to improve the trustworthiness of LLMs outputs.