Energy security, climate change, and growing energy demand issues are moving up on the global political agenda, and contribute to the rapid growth of the renewable energy sector. In this paper we investigate the effects of oil price shocks, and also of uncertainty about oil prices, on the stock returns of clean energy and technology companies. In doing so, we use monthly data that span the period from May 1983 to December 2016, and a bivariate structural VAR model that is modified to accommodate GARCH-in-mean errors. Moreover, we examine the asymmetry of stock responses to oil price shocks of different sizes, with and without oil price uncertainty. Our evidence indicates that oil price uncertainty has no statistically significant effect on stock returns, and that the relationship between oil prices and stock returns is symmetric. Our results are robust to alternative model specifications and stock prices of clean energy companies.