Extremely low-frequency electromagnetic fields (ELF-EMF) have become widespread in various biological studies. Few recent studies have shown that ELF-EMFs can stimulate the secretion of extracellular vesicles (EV) without altering their content and have no adverse effects on the biological properties of the tissue or cells being exposed. Thus, the present study aims to develop a practical coil system capable of generating ELF-EMF. The coil system is designed to meet several constraints imposed by the specialized equipment employed in the biomedical studies, namely, a bioreactor used for cultivating mesenchymal stem cells (MSCs). Firstly, it must be capable of generating very low frequency (VLF) magnetic fields. Secondly, it must provide at least a 3% magnetic field uniformity within a relatively small volume - region of space occupied by a FiberCell Systems C2011 or similar cartridge. Finally, it must be capable of producing a relatively high-intensity magnetic field with a peak-to-peak value of up to 7 mT in the frequency range from 10 to 50 Hz. The size and shape of the high field uniformity regions of different heterogeneity levels provided by the designed coil system are evaluated via numerical simulations. Three different models of varying degrees of complexity are constructed and examined, including the one created using commercially available software Ansys Maxwell. The numerical results obtained using different models are compared showing excellent agreement. Additionally, a prototype of the coil system is fabricated to experimentally verify the theoretical results. The measured data are in keeping with the calculated ones. The fabricated four-coil system is currently utilized in ongoing biological studies.