Bayesian sequencing of radiocarbon dates deals with the problem that in most cases there does not exist an unambiguous way to define the so-called prior function, which represents information in addition to the result of the 14C measurements alone. However, a random choice of a particular prior function can lead to biased results. In this paper, “robust Bayesian analysis,” which uses a whole set of prior functions, is introduced as a more reliable method. The most important aspects of the mathematical foundation and of the practical realization of the method are described. As a general result, robust Bayesian analysis leads to higher accuracy, but paid for with reduced precision. Our investigations indicate that it seems possible to establish robust analysis for practical applications.