Surface plasmon polaritons (SPPs) are electron density waves excited at the interfaces between metals and dielectric materials. Owing to their highly localized electromagnetic fields, they may be used for the transport and manipulation of photons on subwavelength scales. In particular, plasmonic resonant cavities represent an application that could exploit this field compression to create ultrasmall-mode-volume devices. A key figure of merit in this regard is the ratio of cavity quality factor, Q (related to the dissipation rate of photons confined to the cavity), to cavity mode volume, V (refs 10, 11). However, plasmonic cavity Q factors have so far been limited to values less than 100 both for visible and near-infrared wavelengths. Significantly, such values are far below the theoretically achievable Q factors for plasmonic resonant structures. Here we demonstrate a high-Q SPP whispering-gallery microcavity that is made by coating the surface of a high-Q silica microresonator with a thin layer of a noble metal. Using this structure, Q factors of 1,376 +/- 65 can be achieved in the near infrared for surface-plasmonic whispering-gallery modes at room temperature. This nearly ideal value, which is close to the theoretical metal-loss-limited Q factor, is attributed to the suppression and minimization of radiation and scattering losses that are made possible by the geometrical structure and the fabrication method. The SPP eigenmodes, as well as the dielectric eigenmodes, are confined within the whispering-gallery microcavity and accessed evanescently using a single strand of low-loss, tapered optical waveguide. This coupling scheme provides a convenient way of selectively exciting and probing confined SPP eigenmodes. Up to 49.7 per cent of input power is coupled by phase-matching control between the microcavity SPP and the tapered fibre eigenmodes.