  Physically relevant solutions in general relativity often contain spacetime
singularities, which are typically interpreted as a sign of breakdown of the
theory at high densities/curvatures. Hence, there has been a growing interest
in exploring phenomenological scenarios that describe singularity-free black
holes, gravitational collapses, and cosmological models. We examine the metric
put forth by Mazza, Franzin \& Liberati for a rotating regular black hole and
estimate the regularization parameter $l$ based on existing X-ray and
gravitational wave data for black holes. When $l=0$, the solution corresponds
to the singular Kerr solution of general relativity, while a non-zero value of
$l$ yields a regular black hole or a regular wormhole. The analysis reveals
that the available data support a value of $l$ that is close to zero.
