In the transition to a low-carbon economy, climate-resilient investors may be inclined to buy renewable-energy or other low-carbon assets. As the diversification benefits of investment positions in those assets depend on interdependence between their market prices, we explore that interdependence in the European and USA stock markets. We model the dependence structure using bivariate copula functions and evaluate price spillovers between those markets using a conditional quantile dependence approach that accounts for the reciprocal effects of price movements in those markets under normal and extreme market scenarios. Our empirical evidence for the period 2010–2019 indicates that European renewable-energy and low-carbon stocks co-move; upward and downward movements in low-carbon asset prices have sizeable effects on renewable-energy asset prices, and vice versa, although effects are smaller. In contrast, for the USA we find evidence of non-interdependence, with no significant upward or downward price spillover effects between renewable-energy and low-carbon stocks. Our empirical findings provide useful insights for the design of carbon-resilient portfolios and risk management strategies, and also for implementation of public funding policies to support the transition to a low-carbon economy.