We demonstrate laser-written concave hemispherical structures produced on the endfacets of optical fibers that serve as mirror substrates for tunable open-access microcavities. We achieve finesse values of up to 200, and a mostly constant performance across the entire stability range. This enables cavity operation also close to the stability limit, where a peak quality factor of 1.5 × 104 is reached. Together with a small mode waist of 2.3 µm, the cavity achieves a Purcell factor of C ∼ 2.5, which is useful for experiments that require good lateral optical access or otherwise large separation of the mirrors. Laser-written mirror profiles can be produced with a tremendous flexibility in shape and on various surfaces, opening new possibilities for microcavities.