Abstract Geophysical estimates of paleo heat fluxes on the Uranian moons Miranda and Ariel are in the range of 25–75 mW m−2. For a canonical Uranus dissipation factor Q = 18,000, expected equilibrium tidal heating rates for these satellites are less than 6 mW m−2. At least for Ariel, this order-of-magnitude discrepancy can be resolved by positing a low Uranus Q ≈ 103 in the recent past and at the present day. Such a low Q (high dissipation) can be reconciled with an ancient origin of the Uranian satellites if Q is time-dependent, as exemplified by the “resonance-locking” hypothesis, and provides an additional constraint on the interior structure of the planet. A Q of 103 implies present-day migration rates for Miranda and Ariel of 5 and 11 cm yr−1, respectively, potentially detectable via astrometry.