We present a model-agnostic framework for the construction of prediction intervals of insurance claims, with finite sample statistical guarantees, extending the technique of split conformal prediction to the domain of two-stage frequency-severity modeling. The framework effectiveness is showcased with simulated and real datasets using classical parametric models and contemporary machine learning methods. When the underlying severity model is a random forest, we extend the two-stage split conformal prediction algorithm, showing how the out-of-bag mechanism can be leveraged to eliminate the need for a calibration set in the conformal procedure.