This thesis presents the first ever measurement of the noise emitted by magnetic monopoles and the development of an exquisitely sensitive magnetic-field-noise spectrometer based on a superconducting quantum interference device (SQUID) that enabled it. Magnetic monopoles are highly elusive elementary particles exhibiting quantized magnetic charge. The prospects for studying them brightened recently with the theoretical discovery that the thermally excited states in certain classes of magnetic insulators exhibit all the characteristics of magnetic monopoles. Furthermore, in 2018, it was...