Conventional wire bonding in emerging wide bandgap (WBG) semiconductor devices employed in power modules is subjected to failure due to thermo-mechanical stress occurring at the joints. Pressure contact technology improves the reliability of such power modules, eliminating wire bonds between the substrate and components. This paper presents the characteristics and design process of a new type of spring connector in a gallium-nitride (GaN) DC-DC converter for reducing parasitics as well as improving heat dissipation and mechanical stability. Using analytical models and multi-physics finite element method (FEM) simulations, the geometrical design of the spring has been optimized to achieve low parasitics and satisfactory cooling ability, combined with a safe maximum stress. FEM simulations and initial measurement of the optimized spring connector indicate a low inductance (~3 nH) and a low resistance (~5 mΩ).