  Quantum gravitational effects in black hole spacetimes with a cosmological
constant $\Lambda$ are considered. The effective quantum spacetimes for the
black holes are constructed by taking into account the renormalization group
improvement of classical solutions obtained in the framework of Unimodular
Gravity (a theory which is identical to General Relativity at a classical
level). This allows us to avoid the usual divergences associated with the
presence of a running $\Lambda$. The horizons and causal structure of the
improved black holes are discussed taking into account the current
observational bounds for the cosmological constant. It is shown that the
resulting effective quantum black hole spacetimes are always devoid of
singularities.
