High-temperature latent heat thermal energy storage systems offer compact storage solutions, benefiting from the large latent heat of phase change materials. Common challenges in their design process are the low thermal conductivity of the phase change material and the low convective heat transfer between the phase change material and the working fluid. We present a design methodology for a high-temperature latent heat thermal energy storage unit. Eutectic Si-Mg with high thermal conductivity is considered as the phase change material, which is encapsulated in vertical SiC tubes. Charging/discharging is achieved by passing a heat transfer fluid along the encapsulation. In some cases, the flow passage is filled with porous medium to enhance the convective heat transfer between the encapsulated phase change material and the heat transfer fluid. A transient multi-physics model was developed to analyze the performance of the storage unit. The model couples the Brinkman-Forchheimer equations for fluid flow and a local thermal non-equilibrium formulation for the heat transfer, including a P1 approximation to consider the radiation in the porous domain. The apparent heat capacity formulation was used for the domain containing phase change material. A parametric study was conducted to evaluate the unit performance’s sensitivity. These results were used in a multi-criteria optimization to guide the design and sizing of tailored storage units. The results show that practical high-temperature latent heat storage units with an effectiveness as large as 0.95 and maximum storage energy of about 810 MJ/m3 can be achieved. The investigated tubular configuration can be scaled into a thermal energy storage system through in-series or parallel addition of multiple units, providing a straightforward approach to a tailored storage solution.