Survival prediction often involves estimating the time-to-event distribution from censored datasets. Previous approaches have focused on enhancing discrimination and marginal calibration. In this paper, we highlight the significance of conditional calibration for real-world applications, particularly its role in individual decision-making. We propose a method based on conformal prediction that uses the model's predicted individual survival probabilities at observed times. This method effectively improves that model's marginal and conditional calibration, without compromising discrimination. We provide theoretical guarantees for both marginal and conditional calibration and extensively test it across 15 diverse real-world datasets, demonstrating the method's practical effectiveness and versatility in various settings.