High-temperature superconductors (HTS) have attracted increasing attention for their ability to carry very high current densities at relatively high temperatures, enabling the development of compact magnets capable of generating strong magnetic fields. These materials are of particular interest for applications in fusion reactors. This thesis focuses on the electromagnetic behavior of HTS pancake coils, investigated through numerical simulations to analyze how the geometric configuration and the current distribution affect coil performance. The study specifically examines the phenomenon of screening currents, their influence on the central magnetic field, and the dependence of the maximum injectable current on coil geometry. The modeled geometry is comparable in scale to the superconducting components of gyrotrons, although the results obtained have more general relevance.