This paper analyzes δ. CoVaR proposed by Adrian and Brunnermeier (2011) as a tool for identifying/ranking systemically important institutions. We develop a test of significance of δ. CoVaR that allows determining whether or not a financial institution can be classified as being systemically important on the basis of the estimated systemic risk contribution, as well as a test of dominance aimed at testing whether or not, according to δ. CoVaR, one financial institution is more systemically important than another. We provide an empirical application on a sample of 26 large European banks to show the importance of statistical testing when using δ. CoVaR, and more generally also other market-based systemic risk measures, in this context.