A target irradiated with a high power laser pulse, blows off a large amount of charge and as a consequence the target itself becomes a generator of electromagnetic pulses (EMP) owing to high return current flowing to the ground through the target holder. The first measurement of the magnetic field induced by the neutralizing current reaching a value of a few kA was performed with the use of an inductive target probe at the PALS Laser Facility (Cikhardt et al. Rev. Sci. Instrum. 85 (2014) 103507). A full description of EMP generation should contain information on the spatial distribution and temporal variation of the electromagnetic field inside and outside of the interaction chamber. For this reason, we consider the interaction chamber as a resonant cavity in which different modes of EMP oscillate for hundreds of nanoseconds, until the EMP is transmitted outside through the glass windows and EM waves are attenuated. Since the experimental determination of the electromagnetic field distribution is limited by the number of employed antennas, a mapping of the electromagnetic field has to be integrated with numerical simulations. Thus, this work reports on a detailed numerical mapping of the electromagnetic field inside the interaction chamber at the PALS Laser Facility (covering a frequency spectrum from 100 MHz to 3 GHz) using the commercial code COMSOL Multiphysics 5.2. Moreover we carried out a comparison of the EMP generated in the parallelepiped-like interaction chamber used in the Vulcan Petawatt Laser Facility at the Rutherford Appleton Laboratory, against that produced in the spherical interaction chamber of PALS.