  We investigate the quantization of adiabatic charge transport in the
insulating ground state of finite systems. Topological charge pumps are used in
experiments as an indicator of topological order. In the thermodynamic limit
the transport can be related to a topological Berry phase and is thus strictly
quantized. This is no longer true for finite systems. We derive finite-size
corrections to the transport both for non-interacting and interacting systems
and relate them to analytic properties of the single- and many-body Berry
curvature. We find that they depend on the details of experimental realizations
of the pumps. While they can be non-negligible even in large systems, a proper
choice of the pumping protocol can suppress these corrections.
