Algorithmic matches in fielded kidney exchanges do not typically result in an actual transplant. We address the problem of cycles and chains in proposed matches failing after the matching algorithm has committed to them. We show that failure-aware kidney exchange can significantly increase the expected number of lives saved (i) in theory, on random graph models; (ii) on real data from kidney exchange match runs between 2010 and 2014; and (iii) on synthetic data generated via a model of dynamic kidney exchange. This gain is robust to uncertainty over the true underlying failure rate. We design a branch-and-price–based optimal clearing algorithm specifically for the probabilistic exchange clearing problem and show that this new solver scales well on large simulated data, unlike prior clearing algorithms. Finally, we show that failure-aware matching can increase overall system efficiency and simultaneously increase the expected number of transplants to highly sensitized patients, in both static and dynamic models. This paper was accepted by Yinyu Ye, optimization.