ABSTRACT Doing high-precision astrometry on Uranus’ moons is currently quite challenging. No probes will orbit the system before 2040. New high-precision mutual phenomena measurements will only occur in 2050. Besides, Uranus is slowly passing through a sky region without many stars, which makes it difficult to map field of view (FOV) distortions below 50 mas. In this context, the new astrometric technique of mutual approximations comes in handy. It measures central instants at the closest approach between two moving satellites in the sky plane. Measurements are made on small portions of the FOV, benefiting from the so-called precision premium. Approximations and mutual phenomena share geometric principles and parameters, with similar precision in the central instant as indicated by first applications to the Jovian moons. However, mutual phenomena can only be observed at the planet’s equinoxes, while approximations always occur. Central instants do not depend on reference stars and are useful in orbit and ephemeris fittings. Here, we present results for 23 mutual approximations between the five main Uranus satellites observed in Brazil during 2015–2018 with a 1.6 m aperture telescope. Digital coronagraphy mitigated Uranus’ scattered light, improving measurements for Miranda, Ariel and Umbriel. We measured the impact parameter and relative velocity in milliarcseconds for the first time by using a variant of the method. Relative position errors, including Miranda, were 45 mas per coordinate, twice as good as in classical CCD astrometry for this satellite, and comparable to mutual phenomena. This shows the potential of mutual approximations for improving the current orbits and ephemerides of Uranus’ moons.