Renewable energy (RE) technologies are regarded as a solution to the climate impact of buildings, but some of these technologies contain embodied CO2 emissions, which have been ignored in most studies. Previous studies found carbon compensation to be necessary for reaching carbon neutrality as even the least carbon-intensive energy production technologies contain emissions related to manufacturing. The novelty of this study was to combine emission and cost calculations into a single method by including the compensation cost for the carbon footprint in the total life cycle cost (LCC) of carbon-neutral building energy systems. Embodied emissions were included in the carbon footprint of the building energy system in addition to operational emissions. The implemented RE technologies were dimensioned in an optimization loop by minimizing the total LCC of the energy system. The method was tested in a case study. The embodied emissions of the studied RE technology options for the case building accounted for up to 48% of the total carbon footprint, and carbon compensation accounted for 0.3–1.9% of the total LCC. The method was proven to be applicable to the cost-optimal dimensioning of carbon-neutral energy system options and is recommended for use in further studies regarding carbon-neutral building energy systems.