When deciding on the best historic building retrofit, energy savings and thermal comfort can be quantitatively evaluated using an energy model, whereas conservation compatibility is intrinsically qualitative and reflects the perspective of the local heritage authority. We present a methodology that permits finding and comparing optimal retrofits for historic buildings in a multi-perspective and quantitative way. We use an analytic hierarchy process to quantify conservation compatibility by distilling a conservation score from the opinions of 10 experts in the field. This score, along with energy needs for heating and cooling and thermal comfort, are the three targets of a multi-objective optimization aimed at identifying optimal retrofits for a medieval building in the north of Italy, destined to become a museum. Retrofit measures considered were different kinds of external and internal envelope insulation, improvement of airtightness, replacement of windows, and ventilative cooling. The result is a portfolio of optimal retrofits that cover the whole range of conservation compatibility. We show that in the analyzed case heritage preservation is compatible with a four-fold reduction in energy needs at a high thermal comfort level. Even higher energy savings are only achievable at the cost of heritage degradation.