Random survival forests constitute a robust approach to survival modeling, i.e., predicting the probability that an event will occur before or on a given point in time. Similar to most standard predictive models, no guarantee for the prediction error is provided for this model, which instead typically is empirically evaluated. Conformal prediction is a rather recent framework, which allows the error of a model to be determined by a user specified confidence level, something which is achieved by considering set rather than point predictions. The framework, which has been applied to some of the most popular classification and regression techniques, is here for the first time applied to survival modeling, through random survival forests. An empirical investigation is presented where the technique is evaluated on datasets from two real-world applications; predicting component failure in trucks using operational data and predicting survival and treatment of heart failure patients from administrative healthcare data. The experimental results show that the error levels indeed are very close to the provided confidence levels, as guaranteed by the conformal prediction framework, and that the error for predicting each outcome, i.e., event or no-event, can be controlled separately. The latter may, however, lead to less informative predictions, i.e., larger prediction sets, in case the class distribution is heavily imbalanced.