Bayesian *t* tests have become increasingly popular alternatives to null-hypothesis significance testing (NHST) in psychological research. In contrast to NHST, they allow for the quantification of evidence in favor of the null hypothesis and for optional stopping. A major drawback of Bayesian *t* tests, however, is that error probabilities of statistical decisions remain uncontrolled. Previous approaches in the literature to remedy this problem require time-consuming simulations to calibrate decision thresholds. In this article, we propose a sequential probability ratio test that combines Bayesian *t* tests with simple decision criteria developed by Abraham Wald in 1947. We discuss this sequential procedure, which we call *Waldian t test*, in the context of three recently proposed specifications of Bayesian *t* tests. Waldian *t* tests preserve the key idea of Bayesian *t* tests by assuming a prior distribution for the effect size under the alternative hypothesis. At the same time, they control expected frequentist error probabilities, with the nominal Type I and Type II error probabilities serving as upper bounds to the actual expected error rates under the specified statistical models. Thus, Waldian *t* tests are fully justified from both a frequentist and a Bayesian point of view. We highlight the relationship between frequentist and Bayesian error probabilities and critically discuss the implications of conventional stopping criteria for sequential Bayesian *t* tests. Finally, we provide a user-friendly web application that implements the proposed procedure for interested researchers.