A semi-Markov model is a multi-state jump process in which the jump intensities vary based on the current state, calendar time, and duration since the last jump. In the context of life insurance, these models allow for transitions based on age and time since the last transition between states. In this talk, we demonstrate how they can be accurately approximated, in a pathwise sense, using time-homogeneous Markovian jump processes. These are constructed by observing the original model at an increasingly dense set of Poisson arrivals and placing those observations at a different set of independent Poisson times. The primary advantage of our approximation is the existence of closed-form formulae for its transition probabilities, which are not explicitly available in the exact case. In summary, our method simplifies the study of descriptors of semi-Markov models through approximations with homogeneous Markovian jump processes, offering a valuable tool for pricing life insurance policies under such models. This is joint work with Martin Bladt and Andreea Minca.