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To increase the impact that Zero Emission Neighbourhoods (ZEN) can have in the effort to decrease CO2 emissions, the refurbishment of the existing building stock is a parameter that should be considered. The existing literature contains work on optimization models for the energy system of neighbourhoods taking into account emissions but fails to account for the refurbishment of buildings. This paper addresses this option and presents an optimization model for designing a cost-optimal energy system of a ZEN in the context of existing buildings. The model is presented and used in a case study in Norway and compared to a case with linearized binaries. A sensitivity analysis is performed on the cost of refurbishment. With the original refurbishment cost assumptions, it is not chosen by the optimization, contrary to the hydronic. The system relies mainly on PV, solar thermal collectors (ST), a biogas engine, a battery and heat pumps (HP) and heat storage. From 50% of the original refurbishment cost, it is chosen, and the system does not have a biogas engine and a heating grid anymore, but a much bigger battery and more heating technologies inside the buildings. With linearized binaries, the investments are similar to the case with 50% refurbishment cost, but the value of the linearized binaries cannot be used to indicate the share of building to refurbish.