Floating offshore wind represents a new frontier of renewable energies. The absence of a fixed structure allows exploiting wind potential in deep seas, like the Atlantic Ocean and Mediterranean Sea, characterized by high availability and wind potential. However, a floating offshore wind system, which includes an offshore turbine, floating platform, moorings, anchors, and electrical system, requires very high capital investments: one of the most relevant cost items is the floating substructure. This work focuses on the choice of a floating platform that minimizes the global weight, in order to reduce the material cost, but ensuring buoyancy and static stability. Subsequently, the optimized platform is used to define a wind farm located near the island of Pantelleria, Italy in order to meet the island’s electricity needs. A sensitivity analysis to estimate the Levelized Cost Of Energy is presented, analyzing the parameters that influence it most, like Capacity Factor, Weighted Average Capital Cost (WACC) and number of wind turbines.