This paper proposes a detailed analysis of the evolution of Canadian energy systems under some selected EMF (Energy Modeling Forum) 34 scenarios. Our analysis is based on NATEM, an energy model that follows the TIMES approach of the International Energy Agency to represent in detail the energy sector of each of the 13 Canadian provinces and territories. NATEM shows that imposing different renewable penetration constraints for electricity generation has limited impacts outside the electricity sector. In particular, greenhouse gas (GHG) emissions continue to increase over time. Conversely, the imposition of a carbon tax has broader impacts on Canadian energy systems and on GHG emissions that are almost stabilized. However, the level of the carbon tax envisions by the EMF 34 study (increasing to a maximum level of $130 per tonne by 2050) is not high enough, in a Canadian context, to trigger a decrease of GHG emissions over time as mandated by Canadian climate policies.