As power conversion technology is being integrated further into high-reliability environments such as aerospace and electric vehicle applications, a full analysis and understanding of the system's robustness under operating conditions inside and outside the safe-operating-area is necessary. The robustness of power semiconductor devices, a primary component of power converters, has been traditionally evaluated through qualification tests that were developed for legacy silicon (Si) technologies. However, new devices have been commercialized using wide bandgap (WBG) semiconductors including silicon carbide (SiC) and gallium nitride (GaN). These new devices promise enhanced capabilities (e.g., higher switching speed, smaller die size, lower junction capacitances, and higher thermal conductance) over legacy Si devices, thus making the traditional qualification experiments ineffective. This work begins by introducing a new methodology for evaluating the switching robustness of SiC metal-oxide-semiconductor field-effect transistors (MOSFETs). Recent static acceleration tests have revealed that SiC MOSFETs can safely operate for thousands of hours at a blocking voltage higher than the rated voltage and near the avalanche boundary. This work evaluates the robustness of SiC MOSFETs under continuous, hard-switched, turn-off stresses with a dc-bias higher than the device rated voltage. Under these conditions, SiC MOSFETs show degradation in merely tens of hours at 25si{textdegree}C and tens of minutes at 100si{textdegree}C. Two independent degradation and failure mechanisms are unveiled, one present in the gate-oxide and the other in the bulk-semiconductor regions, detected by the increase in gate leakage current and drain leakage current, respectively. The second degradation mechanism has not been previously reported in the literature; it is found to be related to the electron hopping along the defects in semiconductors generated in the switching tests. The comparison with the static acceleration tests reveals that both degradation mechanisms correlate to the high-bias switching transients rather than the high-bias blocking states. The GaN high-electron-mobility transistor (HEMT) is a newer WBG device that is being increasingly adopted at an unprecedented rate. Different from SiC MOSFETs, GaN HEMTs have no avalanche capability and withstand the surge energy through capacitive charging, which often causes significant voltage overshoot up to their catastrophic limit. As a result, the dynamic breakdown voltage (BV) and transient overvoltage margin of GaN devices must be studied to fully evaluate the switching ruggedness of devices. This work characterizes the transient overvoltage capability and failure mechanisms of GaN HEMTs under hard-switched turn-off conditions at increasing temperatures, by using a clamped inductive switching circuit with a variable parasitic inductance. This test method allows flexible control over both the magnitude and the dV/dt of the transient overvoltage. The overvoltage robustness of two commercial enhancement-mode (E-mode) p-gate HEMTs was extensively studied: a hybrid drain gate injection transistor (HD-GIT) with an Ohmic-type gate and a Schottky p-Gate HEMT (SP-HEMT). The overvoltage failure of the two devices was found to be determined by the overvoltage magnitude rather than the dV/dt. The HD-GIT and the SP-HEMT were found to fail at a voltage overshoot magnitude that is higher than the breakdown voltage in the static current-voltage measurement. These single event failure tests were repeated at increasing temperatures (100si{textdegree}C and 150si{textdegree}C), and the failures of both devices were consistent with room temperature results. The two types of devices show different failure behaviors, and the underlying mechanisms (electron trapping) have been revealed by physics-based device simulations. Once this single-event overvoltage failure was established, the device's robustness under repetitive overvoltage and surge-energy events remained unclear; therefore, the switching robustness was evaluated for both the HD-GIT and SP-HEMT in a clamped, inductive switching circuit with a 400 V dc bias. A parasitic inductance was used to generate the overvoltage stress events with different overvoltage magnitude up to 95% of the device's destructive limit, different switching periods from 10 ms to 0.33 ms, different temperatures up to 150si{textdegree}C, and different negative gate biases. The electrical parameters of these devices were measured before and after 1 million stress cycles under varying conditions. The HD-GITs showed no failure or permanent degradation after 1-million overvoltage events at different switching periods, or elevated temperatures. The SP-HEMTs showed more pronounced parametric shifts after the 1 million cycles in the threshold voltage, on-resistance, and saturation drain current. Different shifts were also observed from stresses under different overvoltage magnitudes and are attributable to the trapping of the holes produced in impact ionization. All shifts were found to be recoverable after a relaxation period. Overall, the results from these switching-oriented robustness tests have shown that SiC MOSFETs show a tremendous lifetime under static dc-bias experiments, but when excited by hard-switching turn-off events, the failure mechanisms are accelerated. These results suggest the insufficient robustness of SiC MOSFETs under high bias, hard switching conditions, and the significance of using switching-based tests to evaluate the device robustness. These inspired the GaN-based hard-switching turn-off robustness experiments, which further demonstrated the dynamic breakdown voltage phenomena. Ultimately these results suggest that the breakdown voltage and overvoltage margin of GaN HEMTs in practical power switching can be significantly underestimated using the static breakdown voltage. Both sets of experiments provide further evidence for the need for switching-oriented robustness experiments to be implemented by both device vendors and users, to fully qualify and evaluate new power semiconductor transistors. / Doctor of Philosophy / Power conversion technology is being integrated into industrial and commercial applications with the increased use of laptops, server centers, electric vehicles, and solar and wind energy generation. Each of these converters requires the power semiconductor devices to convert energy reliably and safely. textcolor{black}{Silicon has been the primary material for these devices; however,} new devices have been commercialized from both silicon carbide (SiC) and gallium nitride (GaN) materials. Although these devices are required to undergo qualification testing, the standards were developed for silicon technology. The performance of these new devices offers many additional benefits such as physically smaller dimensions, greater power conversion efficiency, and higher thermal operating capabilities. To facilitate the increased integration of these devices into industrial applications, greater robustness and reliability analyses are required to supplement the traditional tests. The work presented here provides two new experimental methodologies to test the robustness of both SiC and GaN power transistors. These methodologies are oriented around hard-switching environments where both high voltage biases and high conduction current exist and stress the intrinsic semiconductor properties. Experimental evaluations were conducted of both material technologies where the electrical properties were monitored over time to identify any degradation effects. Additional analyses were conducted to determine the physics-oriented failure mechanisms. This work provides insight into the limitations of these semiconductor devices for both device designers and manufacturers as well as power electronic system designers.