Electrification of heating and transportation can be greatly combined with excess energy production from variable renewable energy sources that exist in many geographical islands. Grid interconnections, where available, play a vital role in the energy system as provide the required balance between energy consumption and demand but many limitations emerge due to cable capacity and other technical constraints, which in many cases, lead to curtailment events. With the minimization of the energy exchange through the cable between islands and the mainland, the islands' self-resilience is enhanced. The islands of Samsø and Orkney are used as the case studies where, among others, the specific technical solutions of (a) heat pump districting heating with heat storage, (b) electrolyzer for hydrogen production, and (c) electrical vehicles are examined. The proposed technical solutions are enhanced by Demand Side Management actions utilizing high renewable energy sources availability and curtailment events. The solutions are examined and compared with a reference/current status scenario for each island. This work is based on a detailed model representation, using Modelica language, of the transfer and distribution grid assets, allowing the estimation of the impact of the proposed electrification solutions to the grid level as well as the island level. Simulation results revealed that with the proposed actions in Orkney, annual energy export is reduced by 24 GWh but the corresponding energy imports are slightly increased by 13 GWh, reducing curtailment by 1.4 GWh (77%). As for Samsø, the energy imports are reduced by 5 GWh, while the energy imports increase by 2.0 GWh. Grid losses remain at the same level as before at around 2%, but some distribution lines have significantly lower energy traffic due to higher renewables self-consumption.