  We investigate how the speed of gravitational waves, $c_{GW}$, can be tested
by upcoming black hole ringdown observations. We do so in the context of hairy
black hole solutions, where the hair is associated with a new scalar degree of
freedom, forecasting that LISA and TianQin will be able to constrain deviations
of $c_{GW}$ from the speed of light at the ${\cal O}(10^{-4})$ level from a
single supermassive black hole merger. We discuss how these constraints depend
on the nature of the scalar hair, what different aspects of the underlying
physics they are sensitive to in comparison with constraints derived from
gravitational wave propagation effects, which observable systems will place the
most stringent bounds, and that constraints are expected to improve by up to
two orders of magnitude with multiple observations. This is especially
interesting for dark energy-related theories, where existing bounds from
GW170817 need not apply at lower frequencies and where upcoming bounds from
lower-frequency missions will therefore be especially powerful. As such, we
also forecast analogous bounds for the intermediate-frequency AEDGE and DECIGO
missions. Finally, we discuss and forecast analogous black hole ringdown
constraints at higher frequencies (so from LVK, the Einstein Telescope and
Cosmic Explorer) and in what circumstances they can yield new information on
top of existing constraints on $c_{GW}$. All calculations performed in this
paper are reproducible via a companion Mathematica notebook.
