In this paper, we present numerical tools convenient for the investigation of tokamak discharges with current holes. These tools allow the computation of fixed- and free-boundary equilibria with current holes, their representation in Boozer co-ordinates, the determination of the corresponding magnetic fields, field line tracing and also tracing of guiding centre orbits inside the hole. The numerical methods are tested by using two example configurations with different hole sizes. Furthermore, an equilibrium reconstruction of an ASDEX Upgrade discharge is performed. The motional Stark effect polarization angles of this discharge, which indicate a small current hole in the plasma centre, are reproduced by a numerical fit of various equilibrium parameters including pressure profile, rotational transform profile and poloidal coil currents. The resulting plasma parameters lie well inside the experimental error margins.