the development of free probability theory has drawn much inspiration from its deep and far reaching analogy with classical probability theory. the same holds for its operator-valued extension, where the fundamental notion of free independence is generalized to free independence with amalgamation as a kind of conditional version of the former. its development naturally led to operator-valued free analogues of key and fundamental limiting theorems such as the operator-valued free central limit theorem due to voiculescu and results about the asymptotic behaviour of distributions of matrices with operator-valued entries. in this talk, we show berry-esseen bounds for such limit theorems. the estimates are on the level of operator-valued cauchy transforms and the l{\'e}vy distance. we address also the multivariate setting for which we consider linear matrix pencils and noncommutative polynomials as test functions. the estimates are in terms of operator-valued moments and yield the first quantitative bounds on the l{\'e}vy distance for the operator-valued free clt. this also yields quantitative estimates on joint noncommutative distributions of operator-valued matrices having a general covariance profile. this is a joint work with tobias mai.