A large deployment of energy storage solutions will be required by the stochastic and non-controllable nature of most renewable energy sources when planning for higher penetration of renewable electricity into the energy mix. Various solutions have been suggested for dealing with medium- and long-term energy storage. Hydrogen and ammonia are two of the most frequently discussed as they are both carbon-free fuels. In this paper, the authors analyse the energy and cost efficiency of hydrogen and ammonia-based pathways for the storage, transportation, and final use of excess electricity from an offshore wind farm. The problem is solved as a linear programming problem, simultaneously optimising the size of each problem unit and the respective time-dependent operational conditions. As a case study, we consider an offshore wind farm of 1.5 GW size located in a reference location North of Scotland. The energy efficiency and cost of the whole chain are evaluated and compared with competitive alternatives, namely, batteries and liquid hydrogen storage. The results show that hydrogen and ammonia storage can be part of the optimal solution. Moreover, their use for long-term energy storage can provide a significant, cost-effective contribution to an extensive penetration of renewable energy sources in national energy systems.