Accurate models of patient survival probabilities provide important information to clinicians prescribing care for life-threatening and terminal ailments. A recently developed class of models -- known as individual survival distributions (ISDs) -- produces patient-specific survival functions that offer greater descriptive power of patient outcomes than was previously possible. Unfortunately, at the time of writing, ISD models almost universally lack uncertainty quantification. In this paper we demonstrate that an existing method for estimating simultaneous prediction intervals from samples can easily be adapted for patient-specific survival curve analysis and yields accurate results. Furthermore, we introduce both a modification to the existing method and a novel method for estimating simultaneous prediction intervals and show that they offer competitive performance. It is worth emphasizing that these methods are not limited to survival analysis and can be applied in any context in which sampling the distribution of interest is tractable. Code is available at https://github.com/ssokota/spie.