Current solar flare predictions often lack precise quantification of their reliability, resulting in frequent false alarms, particularly when dealing with datasets skewed towards extreme events. To improve the trustworthiness of space weather forecasting, it is crucial to establish confidence intervals for model predictions. Conformal prediction, a machine learning framework, presents a promising avenue for this purpose by constructing prediction intervals that ensure valid coverage in finite samples without making assumptions about the underlying data distribution. In this study, we explore the application of conformal prediction to regression tasks in space weather forecasting. Specifically, we implement full-disk solar flare prediction using images created from magnetic field maps and adapt four pre-trained deep learning models to incorporate three distinct methods for constructing confidence intervals: conformal prediction, quantile regression, and conformalized quantile regression. Our experiments demonstrate that conformalized quantile regression achieves higher coverage rates and more favorable average interval lengths compared to alternative methods, underscoring its effectiveness in enhancing the reliability of solar weather forecasting models.