Purpose The paper investigates factors that contribute to small and medium enterprises (SMEs) surviving major exogenous shocks. Global crises such as the coronavirus disease 2019 (COVID-19) have increasingly heightened scholarly interest in post-crises responses. However, studies that compare the relative responses to external shocks and the outcomes for SMEs operating in different institutional settings are limited. We examine the relative degrees of success European and African SMEs experienced in avoiding the worst consequences of the COVID-19 pandemic.Design/methodology/approachWe use the resource dependency theory (RDT) with variants of institutional theory since the RDT has been shown in practice to have greater explanatory power when used in this way. We augment our framework with a feminist theory dimension. To test our hypotheses, we apply regression analyses using cross-sectional data from the World Bank Enterprise Surveys (WBES), which include responses from private enterprises in 26 European and eight African countries. We construct our data by combining the COVID-19 follow-up surveys with relevant firm-specific characteristics from the WBES conducted in 2020–2021 using firm-specific unique IDs. After removing the firms with missing observations, the sample number of SMEs is 15,178.Findings Our empirical findings support the theoretically posited positive effects of innovativeness, institutional connectedness and governance capability on SMEs’ survival in the face of external shocks. Further, we confirm the importance of firm-specific characteristics (financial status, size and age) for SMEs’ survival. Female-owned SMEs are more likely to suffer during COVID-19, especially in Africa. The results are more nuanced when we consider industry specificity and heterogeneity of government support.Originality/value Our article helps answer the theoretical (and policy-relevant) question of whether SMEs that are resilient to major exogenous shocks may share certain characteristics despite operating in different institutional environments. If that is so, then it may be that lessons from one continent may have at least some relevance for the other. Our approach’s broad value lies in its capacity to test the degree to which established bodies of theory developed in the Northern Hemisphere may be deployed in Africa, well beyond the contexts which provided their initial empirical basis. This paper also contributes to the literature on the effect of environmental-change shocks on entrepreneurship performance outcomes.