The purpose of the work is the development of the methodological approach to the evaluation of the scientific performance of universities on the basis of the institutional economic theory. The novelty of the work is that the author’s technique of quantitative assessment of the scientific performance of universities, in contrast to the known ones, allows revealing the problems of institutional support of scientific activity. During the research, I applied the methods of the system, logical and economic analysis. For processing empirical information, I used the methods of statistical analysis, correlation analysis. As a result of the research, the author has identified the institutions of scientific performance of the university, offered the criteria of the efficiency of these institutions. The universities of the Ural Federal District are grouped according to the parameters of the quality of the institutions of scientific performance (and according to the existence of effective institutions, institutional traps, institutional dysfunctions).