Transitioning to medium-voltage (MV) power electronics presents a significant opportunity for reducing ampacity requirements, and therefore cable weight, for large transportation systems such as electric ships and trains. MV silicon-carbide (SiC) semiconductors are especially attractive in this regard due to their increased edge rates compared to traditional silicon-based (Si-based) semiconductors. These device-level advantages enable higher switching speeds and lower switching losses, which translate to increased efficiency and power density at the system level. However, transitioning to MV SiC power electronics also presents several challenges which must be understood and addressed before this technology achieves wide-scale market adoption. This dissertation provides a systematic evaluation of one of the most important of these challenges: instrumenting and measuring MV SiC devices and systems. This dissertation demonstrates this challenge in the context of MV SiC device characterization experiments as well as converter applications involving MV SiC devices. Through targeted case studies, recommendations are provided and solutions are demonstrated for safely performing high-fidelity current, voltage, efficiency, and electromagnetic interference (EMI) measurements for SiC-based systems operating at elevated voltages. These recommendations and practices are especially valuable in light of the significant limitations of commercially available instruments for evaluation of MV devices and systems. The metrology solutions presented in this dissertation are demonstrated through two case studies. The first case study involves a double-pulse test (DPT) platform designed for MV SiC device characterization experiments. The second case study involves a single-phase, neutral-point-clamped (NPC) inverter designed for continuous operation. For both studies, details are provided regarding the design, fabrication, and experimental evaluation of these circuits, with specific emphasis on the associated metrology challenges. The DPT platform is used to characterize an example MV SiC multi-chip power module (MCPM) at conditions up to 2.5 kV and 0.8 kA. The NPC inverter, which is implemented using the same MV SiC MCPMs discussed in the first case study, is demonstrated during continuous operation at conditions up to 5 kV and 20 kW. The performance of the NPC inverter is also evaluated when operated with SiC-based and with traditional Si-based MCPMs. Comparison of these two configurations provides a compelling demonstration of the advantages of adopting SiC semiconductors in MV applications, and demonstrates that the metrology challenges discussed throughout this dissertation can be effectively overcome.