Microgrids can increase the security of supply of electricity systems, and also can support to achieve a carbon-free electricity system in the areas where the security of supply is close to 100%. Besides technical aspects, characteristics such as optimum design, cost consideration factors and different technologies have to be addressed. Meanwhile, there are challenges for cost-effective carbon-free microgrids due to intermittency and fluctuation issues. Therefore, energy storage technologies have been proposed to facilitate the transition to a CO2 emission-free solution. This paper proposes a framework to analyze the feasibility of energy storage technologies for microgrids. The method considers input requirements and issues such as economic feasibility, energy technology selection, renewability assessment, storage capability, etc. The method is applied in a case of a Danish island to achieve the overall goal of having a 100% renewable portfolio. Several storage technologies are evaluated with three defined criteria. The result shows that it is possible to obtain a feasible solution with the application of energy storage technologies in the island with a drawback of increasing the final energy cost.