The paper defends the thesis that institutional virtue is properly modeled as a “consensual” property, along the lines of the Lehrer-Wagner model of consensus (LWC). In a first step, it is argued that institutional virtue is not exhausted by duty-fulfilling, since institutions, contrary to natural individuals, are designed to fulfill duties. To avoid the charge of vacuity, virtue, if attributed to institutions, must be able to motivate supererogatory action. In a second step, the paper argues against discontinuity of institutional virtue with individual virtue. Two main arguments for discontinuity of collective properties display serious shortcomings when applied to virtues of institutions. Given that motivation for supererogatory action is neither inferred from statutory duties nor accommodates a right of reprobation, modeling institutional virtue on collective rationality or explaining it in terms of joint commitment both prove problematic. In a third step, it is argued that LWC has the explanatory potential to account for institutional virtue. Due to its main features, iteration and evaluation, it provides a non-trivial analysis of continuity and thereby satisfies basic constraints on the notion of genuine institutional virtue.