Superconductors expel magnetic fields, a phenomenon known as the Meissner effect. This effect makes it notoriously difficult to predict the magnetic field around a superconductor. One successful way of calculating these fields is through conformal mappings; coordinate transformations that preserve Maxwell's equations of magnetic fields in free space. These were first described by Norris and later improved by Brandt. In this bachelor thesis, conformal mappings are introduced and applied to 8 situations of magnetic field screening of an increasingly complex nature. We look at the screening of applied magnetic fields and of magnetic fields due to a bias current running through a wire itself. We later compare these results with experimental observations of the Van der Sar lab in Delft and measurements from other papers.