With the widespread application of large language models (LLMs) in the field of code intelligence, increasing attention has been paid to the reliability and controllability of their outputs in code reasoning tasks. Confidence estimation serves as an effective and convenient approach for evaluating these aspects. This paper proposes a confidence analysis and enhancement framework for LLMs tailored to code reasoning tasks. We conduct a comprehensive empirical study on the confidence reliability of mainstream LLMs across different tasks, and further evaluate the effectiveness of techniques such as prompt strategy optimisation and mathematical calibration (e.g., Platt Scaling) in improving confidence reliability. Our results show that DeepSeek-Reasoner achieves the best performance across various tasks, outperforming other models by up to $0.680$, $0.636$, and $13.652$ in terms of ECE, Brier Score, and Performance Score, respectively. The hybrid strategy combining the reassess prompt strategy and Platt Scaling achieves improvements of up to $0.541$, $0.628$, and $15.084$ over the original performance in the aforementioned three metrics. These results indicate that models with reasoning capabilities demonstrate superior confidence reliability, and that the hybrid strategy is the most effective in enhancing the confidence reliability of various models. Meanwhile, we elucidate the impact of different task complexities, model scales, and strategies on confidence performance, and highlight that the confidence of current LLMs in complex reasoning tasks still has considerable room for improvement. This study not only provides a research foundation and technical reference for the application of confidence in LLM-assisted software engineering, but also points the way for future optimisation and engineering deployment of confidence mechanisms.