This paper analyzes the economic potential of Power-to-Gas (PtG) as a source of flexibility in electricity markets with both high shares of renewables and high external demand for hydrogen. The contribution of this paper is that it develops and applies a short-term (hourly) partial equilibrium model of integrated electricity and hydrogen markets, including markets for green certificates, while using a welfare-economic framework to assess the market outcomes. We find that strongly increasing the share of renewable electricity makes electricity prices much more volatile, while the presence of PtG reduces this price volatility. However, a large demand for hydrogen from outside the electricity sector reduces the impact of PtG on the volatility of electricity prices. In a scenario with a high external hydrogen demand, PtG can deliver positive benefits for some groups as it can provide hydrogen at lower costs than Steam Methane Reforming (SMR) during hours when electricity prices are low, but these positive welfare effects are outweighed by the fixed costs of PtG assets plus the costs of replacing a less expensive energy carrier (natural gas) with a more expensive one (hydrogen). Investments in PtG are profitable from a social-welfare perspective when the induced reduction in carbon emissions is valued at 150–750 euro/ton. Hence, at lower carbon prices, PtG can only become a valuable provider of flexibility when installation costs are significantly reduced and conversion efficiencies of electrolysers increased.