Causal discovery procedures aim to deduce causal relationships among variables in a multivariate dataset. While various methods have been proposed for estimating a single causal model or a single equivalence class of models, less attention has been given to quantifying uncertainty in causal discovery in terms of confidence statements. The primary challenge in causal discovery is determining a causal ordering among the variables. Our research offers a framework for constructing confidence sets of causal orderings that the data does not rule out. Our methodology applies to structural equation models that may be uniquely identified and is based on a residual bootstrap procedure to test the goodness-of-fit of causal orderings. We demonstrate the asymptotic validity of the confidence set constructed using this goodness-of-fit test and explain how the confidence set may be used to form conservative sets of ancestral relationships as well as confidence intervals for causal effects that consider model uncertainty.