Introduction. Transcranial magnetic stimulation (TMS) is used for treating neurological disorders. Rapid pulses of magnetic field are delivered via a high-current coil situated over the scalp and induce an electric field in the brain. There has been limited fundamental scientific research on TMS and to progress it would be ideal to mimic the electric field of human TMS with mice. Animal models provide good mechanistic insight, but their use is hindered by lack of stimulating coils comparable in focus and intensity with human stimulation. Methods. We outline the engineering challenges in producing appropriate coils. It is unclear what should be optimized in the design of a mouse coil. We model the electric field, heat generation and ring-down time for cylindrical coils and use results to select a coil design consisting of 70 turns of 0.4. mm diameter copper wire wrapped around a 5 mm diameter soft ferrite core. Results and Discussion. While the magnetic flux density scales as the reciprocal of length-scale, the electric field does not scale with length, meaning that a large current is required to mimic the electric field of humans. To maximize electric field, one must minimize the coil's inductance resulting in reduced ring-down time for the coil and significant heating. A ferrite core allows ring-down time to remain high and reduces heating. Our coil gave 180 mT at 30 V supply, with a temperature increase of 5 degrees C after 1200 pulses at 5 Hz. The B-field below the core has a full-width-at-half-maximum of 6 mm, similar in size to a mouse brain. Conclusions. We have produced a mouse coil that offers increased B-field and reduced heating. There is considerable scope for improving electric field, but further physical analysis may lead to field strength more similar to that obtained in human TMS.