Motivated by the increasing use of external instruments to identify structural vector autoregressions (SVARs), we develop algorithms for exact finite sample inference in this class of time series models, commonly known as proxy-SVARs. Our algorithms make independent draws from the normal-generalizednormal family of conjugate posterior distributions over the structural parameterization of a proxy-SVAR. Importantly, our techniques can handle the case of set identification and hence they can be used to relax the additional exclusion restrictions unrelated to the external instruments often imposed to facilitate inference when more than one instrument is used to identify more than one equation as in Mertens and Montiel-Olea (2018).