Coaxial microcavities etched into the surface of a doped silicon substrate are shown to support localized surface plasmon resonances at terahertz frequencies. The underlying mechanism involves coupling freely propagating terahertz waves with surface plasmon polaritons (SPPs), which propagate in a coaxial mode along the cavity walls in the axial direction. A Fabry–Pérot resonance is built up when the SPP wavenumber appropriately relates to the cavity depth. Owing to the Ohmic loss of the silicon at terahertz frequencies, the energy of the resonating SPPs is largely dissipated, leading to a modified reflection spectrum. Strong field enhancement is observed inside the cavities at resonance. The theoretical analysis is supported by numerical and experimental results. This study is a promising pathway for development of terahertz devices with applications in the areas of photonic integrated circuits, molecular sensing, and subwavelength imaging.