This paper presents the details of a study performed to investigate the feasibility of a wave energy system made up of a number of Weptos wave energy converters (WECs) and sets of batteries, to provide the full energy demands of a small island in Denmark. Two different configurations with 2 and 4 Weptos machines respectively with a combined installed power of 750 kW (and a capacity factor of 0.2) are presented. One full year simulation, based a detailed hourly analysis of the power consumption and wave energy resource assessment in the surrounding sea, is used to demonstrate that both configurations, supplemented by a 3 MWh battery bank and a backup generator, can provide the energy needs of the island. The proposed configurations are selected on the basis of a forecast optimization of price estimates for the individual elements of the solutions. The simulations show that Weptos WECs actually deliver 50% more than average consumption over the year, but due to the imbalance between consumption and production, this is not enough to cover all situations, which necessitates a backup generator that must cover 5–7% of consumption, in situations where there are too few waves and the battery bank is empty.