One of the most important factors in successful upper limb prostheses is the socket design. Sockets must be individually fabricated to arrive at a geometry that suits the user's morphology and appropriately distributes the pressures associated with prosthetic use across the residual limb. In higher levels of amputation, such as transhumeral, this challenge is amplified as prosthetic weight and the physical demands placed on the residual limb are heightened. Yet, in the upper limb, socket fabrication is largely driven by heuristic practices. An analytical understanding of the interactions between the socket and residual limb is absent in literature. This work describes techniques, adapted from lower limb prosthetic research, to empirically characterize the pressure distribution occurring between the residual limb and well-fit transhumeral prosthetic sockets. A case series analyzing the result of four participants with transhumeral amputation is presented. A Tekscan VersaTek pressure measurement system and FaroArm Edge coordinate measurement machine were employed to capture socket-residual limb interface pressures and geometrically register these values to the anatomy of participants. Participants performed two static poses with their prosthesis under two separate loading conditions. Surface pressure maps were constructed from the data, highlighting pressure distribution patterns, anatomical locations bearing maximum pressure, and the relative pressure magnitudes. Pressure distribution patterns demonstrated unique characteristics across the four participants that could be traced to individual socket design considerations. This work presents a technique that implements commercially available tools to quantitatively characterize upper limb socket-residual limb interactions. This is a fundamental first step toward improved socket designs developed through informed, analytically-based design tools.