Plasmonics provides great promise for nanophotonic applications. However, the high optical losses inherent in metal-based plasmonic systems have limited progress. Thus, it is critical to identify alternative low-loss materials. One alternative is polar dielectrics that support surface phonon polariton (SPhP) modes, where the confinement of infrared light is aided by optical phonons. Using fabricated 6H-silicon carbide nanopillar antenna arrays, we report on the observation of subdiffraction, localized SPhP resonances. They exhibit a dipolar resonance transverse to the nanopillar axis and a monopolar resonance associated with the longitudinal axis dependent upon the SiC substrate. Both exhibit exceptionally narrow linewidths (7–24 cm–1), with quality factors of 40–135, which exceed the theoretical limit of plasmonic systems, with extreme subwavelength confinement of (λres 3/V eff)1/3 = 50–200. Under certain conditions, the modes are Raman-active, enabling their study in the visible spectral range. These observations promise to reinvigorate research in SPhP phenomena and their use for nanophotonic applications.