Ultralow-loss concave micromirrors with radius of curvature below 60 mu m were fabricated by laser ablation and reflective coatings. A 10-mu m-long microcavity with a mode volume of 40 mu m(3) was set up with two such mirrors, and the cavity linewidth was measured both spectrally and temporally. The smallest linewidth obtained was 96 MHz, corresponding to a quality factor of 3.3 x 10(6) and a finesse in excess of 1.5 x 10(5). With these parameters, we estimate that a variety of solid-state quantum emitters coupled to the cavity may enter the strong coupling regime. (C) 2010 Optical Society of America