We develop methods for robust Bayesian inference in structural vector autoregressions (SVARs) where the impulse responses or forecast error variance decompositions of interest are set-identiﬁed using external instruments (or ‘proxy SVARs’). Existing Bayesian approaches to inference in proxy SVARs require researchers to specify a single prior over the model’s parameters. When parameters are set-identiﬁed, a component of the prior is never updated by the data. Giacomini and Kitagawa (2018) propose a method for robust Bayesian inference in set-identifed models that delivers inference about the identiﬁed set for the parameter of interest. We extend this approach to proxy SVARs, which allows researchers to relax potentially controversial point-identifying restrictions without having to specify an unrevisable prior. We also explore the eﬀect of instrument strength on posterior inference. We illustrate our approach by revisiting Mertens and Ravn (2013) and relaxing the assumption that they impose to obtain point identiﬁcation.