This study was aimed at developing a cognitive—econometric model for assessing the effectiveness of the current governmental policies to support enterprises in Russia in the context of pandemic propagation. Using the Granger test and correlation analysis, we formed a system of key indicators that characterizes the economic development of SMEs (small and medium-sized enterprises) in Russia. Based on the revealed causal relationships and correlation coefficients, a model describing the impact of public policy support instruments on SME economic development was built using cognitive modeling. By means of the additive convolution method, the correlation coefficient between the Russia Small Business Index (RSBI) and the COVID-19 prevalence rate was used to predict the 2020 year-end RSBI value. Regarding the RSBI index forecast, the effectiveness of instruments of the state support for SMEs was evaluated. It was determined how much these indicators of the anti-crisis package of measures should change to increase SMEs’ business activities. The developed cognitive model can be utilized by private and governmental institutions to continuously monitor the effectiveness of public policies that support SMEs. It can also be used as a preventive indicator to evaluate the impact of the anti-crisis measures during pandemics and in the case of other exogenous risks threatening SMEs. The originality of the research results was determined by the econometric methods applied to empirically assess the effectiveness and degree of impact of governmental measures on the operation of SMEs under conditions of uncertainty. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.