Prior-fitted networks (PFNs) have emerged as promising foundation models for prediction from tabular data sets, achieving state-of-the-art performance on small to moderate data sizes without tuning. While PFNs are motivated by Bayesian ideas, they do not provide any uncertainty quantification for predictive means, quantiles, or similar quantities. We propose a principled and efficient method to construct Bayesian posteriors for such estimates based on Martingale Posteriors. Several simulated and real-world data examples are used to showcase the resulting uncertainty quantification of our method in inference applications.