Finite-frequency H₂ analysis is relevant to a number of problems in which a priori information is available on the frequency domain of interest. This paper addresses the problem of analyzing robust finite-frequency H₂ performance of systems with structured uncertainties. An upper bound on this measure is provided by exploiting convex optimization tools for robustness analysis and the notion of finite-frequency Gramians. An application to a comfort analysis problem for an aircraft aeroelastic model is presented.