This work presents an approach to optimally designing a composite with thermal conductivity enhancers infiltrated with phase change material based on figure of merit (FOM) for thermal management of portable electronic devices. The FOM defines the balance between effective thermal conductivity and energy storage capacity. In this study, thermal conductivity enhancers are in the form of a honeycomb structure. Thermal conductivity enhancers are often used in conjunction with phase change material to enhance the conductivity of the composite medium. Under constrained heat sink volume, the higher volume fraction of thermal conductivity enhancers improves the effective thermal conductivity of the composite, while it reduces the amount of latent heat storage simultaneously. This work arrives at the optimal design of composite for electronic cooling by maximizing the FOM to resolve the stated tradeoff. In this study, the total volume of the composite and the interfacial heat transfer area between the phase change material and thermal conductivity enhancers are constrained for all design points. A benchmarked two-dimensional direct computational fluid dynamics model was employed to investigate the thermal performance of the phase change material and thermal conductivity enhancer composite. Furthermore, assuming conduction-dominated heat transfer in the composite, a simplified effective numerical model that solves the single energy equation with the effective properties of the phase change material and thermal conductivity enhancer has been developed. The effective properties like heat capacity can be obtained by volume averaging; however, effective thermal conductivity (required to calculate FOM) is unknown. The effective thermal conductivity of the composite is obtained by minimizing the error between the transient temperature gradient of direct and simplified model by iteratively varying the effective thermal conductivity. The FOM is maximized to find the optimal volume fraction for the present design.