We review the question of quantum consistency of $ \newcommand{\N}{{{\mathcal N}}} \N=4$ conformal supergravity in 4 dimensions. The UV divergences and anomalies of the standard ('minimal') conformal supergravity where the complex scalar $ \newcommand{\vp}{\varphi} \vp$ is not coupled to the Weyl graviton kinetic term can be cancelled by coupling this theory to $ \newcommand{\N}{{{\mathcal N}}} \N=4$ super Yang–Mills with gauge group of dimension 4. The same turns out to be true also for the 'non-minimal' $ \newcommand{\N}{{{\mathcal N}}} \N=4$ conformal supergravity with the action (recently constructed (Butter et al 2017 Phys. Rev. Lett. 118 081602)) depending on an arbitrary holomorphic function $ \newcommand{\vp}{\varphi} f(\vp)$ . The special case of the 'non-minimal' conformal supergravity with $ \newcommand{\vp}{\varphi} f= {\rm e}^{2\vp}$ appears in the twistor-string theory. We show that divergences and anomalies do not depend on the form of the function f and thus can be cancelled just as in the 'minimal' $f=1$ case by coupling the theory to four $ \newcommand{\N}{{{\mathcal N}}} \N=4$ vector multiplets.