This paper presents the concept design phases of a human-centered design process, which focuses on user experience (UX) goals. This process was conducted to design a future human-machine interface (HMI) prototype for operating semi-autonomous drone fleets. The aim of the process was to determine an optimal level of automation and UX for the HMI with a combination of benchmarking existing solutions, definition of novel concepts, and co-design with users. Interviews with expert drone pilots identified user requirements for the future HMI, including pre-flight planning tools, real-time telemetry data, and post-flight analysis features. A Design Sprint workshop generated initial UX goals and HMI solutions, focusing on two use cases: blood delivery and network coverage measurement. Low-fidelity wireframe displays were developed into an interactive HMI prototype, which was refined through heuristic evaluations and UX studies. The UX studies showed that three out of the five chosen UX goals were fulfilled with the utilized HMI prototype version. Future work will need to focus on integrating the solution into an operational ground control station and conducting further user validations, with particular attention to supporting the UX goals of calmness in operation and experience of required level of situational awareness.