This paper introduces a new method called steppingstone sampling (SS) for estimating the marginal likelihood in Bayesian phylogenetic model selection. The marginal likelihood is crucial for comparing different evolutionary models, and it is often estimated using the harmonic mean (HM) method, which is biased and can overestimate the true marginal likelihood. The thermodynamic integration (TI) method is more accurate but computationally intensive. SS combines elements of TI and importance sampling, using importance sampling to estimate ratios of marginal likelihoods. The authors compare the performance of SS with TI and HM through simulations and real data analyses. They find that SS and TI provide more accurate estimates of the marginal likelihood compared to HM, and SS can sometimes choose simpler models due to its ability to penalize complex models more effectively. The paper concludes that HM should not be used for model selection in phylogenetics if more accurate alternatives like SS or TI are available.This paper introduces a new method called steppingstone sampling (SS) for estimating the marginal likelihood in Bayesian phylogenetic model selection. The marginal likelihood is crucial for comparing different evolutionary models, and it is often estimated using the harmonic mean (HM) method, which is biased and can overestimate the true marginal likelihood. The thermodynamic integration (TI) method is more accurate but computationally intensive. SS combines elements of TI and importance sampling, using importance sampling to estimate ratios of marginal likelihoods. The authors compare the performance of SS with TI and HM through simulations and real data analyses. They find that SS and TI provide more accurate estimates of the marginal likelihood compared to HM, and SS can sometimes choose simpler models due to its ability to penalize complex models more effectively. The paper concludes that HM should not be used for model selection in phylogenetics if more accurate alternatives like SS or TI are available.