This work proposes a framework for the robust design of multi-energy systems when limited information on the input data is available. The optimal design of a decentralized system involving renewable energy sources and energy storage technologies is considered by formulating a mixed integer linear program that determines the optimal selection, size, and operation of the system to provide energy to an end user, while minimizing its total annual costs and CO2 emissions. Different aspects related to the feasibility and the optimality resulting when operating the multi-energy system on input data different than those used for the design are studied. Input data include weather conditions, energy demands and energy prices. First, considering a single input scenario, we define the resolution required to describe the time profiles of the input data. To do so, we aggregate hourly-resolved yearly time-series through a different number of typical design days, and we define the minimum number of typical design days necessary to obtain feasible and optimal system designs when these are operated on the original input profiles. Next, the uncertainty of weather conditions and energy demands is analyzed. This is described through several scenarios, which are created by combining different climate models, greenhouse gas emissions forecasts and models of buildings. The system configurations obtained with one of these scenarios are evaluated by introducing performance indicators that quantify the robustness and the cost optimality attained when operating the selected design on all other possible scenarios. Furthermore, correlations between performance indicators, structure and size of the system, and relevant characteristics of the input scenarios are identified. Based on this analysis, a robust scenario is defined, which requires information on the average scenario only, and its performance is compared against those of the average and of the worst-case scenarios when used to design a multi-energy system. Several designs are investigated, focusing on the minimization of costs and CO2 emissions, showing that the proposed robust scenario allows obtaining a robust and optimal system design through a deterministic optimization problem, hence maintaining the computation complexity at a minimum. Despite the higher robustness and cost optimality, slightly higher CO2 emissions are observed than the average and the worst-case scenarios. The proposed method is illustrated by performing the optimal design of a multi-energy system providing electricity and heat to a Swiss urban neighborhood, typical of the city of Zurich.