We develop methods for robust Bayesian inference in structural vector autoregressions (SVARs) where the parameters of interest are set-identiﬁed using external instruments, or ‘proxy SVARs’. Set-identiﬁcation in these models typically occurs when there are multiple instruments for multiple structural shocks. Existing Bayesian approaches to inference in proxy SVARs require researchers to specify a single prior over the model’s parameters, but, under set-identiﬁcation, a component of the prior is never revised. We extend the robust Bayesian approach to inference in set-identiﬁed models proposed by Giacomini and Kitagawa (2018) – which allows researchers to relax potentially con-troversial point-identifying restrictions without having to specify an unrevisable prior – to proxy SVARs. We provide new results on the frequentist validity of the approach in proxy SVARs. We also explore the eﬀect of instrument strength on inference about the identiﬁed set. We illustrate our approach by revisiting Mertens and Ravn (2013) and relaxing the assumption that they impose to obtain point identiﬁcation.