The recent low CO2 prices in the European Union Emission Trading Scheme (EU ETS) have triggered a discussion whether the EU ETS needs to be adjusted. We study the effects of CO2 price floors and a price ceiling on the dynamic investment pathway of two interlinked electricity markets (loosely based on Great Britain, which already has introduced a price floor, and on Central Western Europe). Using an agent-based electricity market simulation with endogenous investment and a CO2 market (including banking), we analyse the cross-border effects of national policies as well as system-wide policy options. A common, moderate CO2 auction reserve price results in a more continuous decarbonisation pathway. This reduces CO2 price volatility and the occurrence of carbon shortage price periods, as well as the average cost to consumers. A price ceiling can shield consumers from extreme price shocks. These price restrictions do not cause a large risk of an overall emissions overshoot in the long run. A national price floor lowers the cost to consumers in the other zone; the larger the zone with the price floor, the stronger the effect. Price floors that are too high lead to inefficiencies in investment choices and to higher consumer costs.