This paper examines the ability of nanosecond repetitively pulsed (NRP) plasma discharges to improve stabilization and extend the blow-off limit of lean premixed methane-air swirl flames at pressures up to 5 bar. The effect of two discharge regimes, NRP glows and NRP sparks, was investigated. The electrical characterization of the discharges was performed and direct images at 60 Hz of the flames, with and without NRP discharges, were collected to assess the effect of the discharges on flame stabilization. Results showed that NRP discharges efficiently extended the lean blow-off and stability limits of premixed methane-air swirl flames, at pressures up to 5 bar. These results were obtained for a ratio of NRP discharge power to flame thermal power of 0.7% or less. Moreover, the peak voltage necessary to maintain constant this power ratio did not increase linearly with increased pressure, even though the reduced electric field should linearly decrease with the pressure. It was also observed that the relative effectiveness of the NRP glows and NRP sparks changed by increasing the pressure. Based on discharge physics and current knowledge of the effect of pressure on the electrical properties of flames, explanations for these results are proposed.