In this thesis I will discuss the development, construction and testing of a sub-Kelvin Q-band electron paramagnetic resonance (EPR) spectrometer and optically detected magnetic resonance (ODMR) of wide bandgap semiconductors at Q-band. The sub-Kelvin EPR spectrometer was developed to be integrated into a standard commercial system. Characterisation of the cryogenics and microwave components of the spectrometer will be discussed as well as the design and adaptations made to enable EPR experiments to be performed below 1 K. A waveguide thermal break design, previously only used in detectors for the cosmic microwave background radiation, was optimised using ANSYS High frequency structure simulator (HFSS) to operate at Q-band and was built and tested in this spectrometer. The sub-Kelvin EPR spectra of Cr3+ in Al2O3 and [Cr12O9(OH)3(O2CCMe3)15] were obtained. The resonant cavity of the spectrometer was also successfully tested at room temperature, with a pulsed microwave bridge, paving the way for further development of the system to enable sub-Kelvin pulsed EPR. A home-built Q-band ODMR spectrometer was used to investigate the wide band gap semiconductors ZnO and InGaN/GaN multiple quantum wells (MQWs). The ZnO was a natural crystal, and used to characterise the spectrometer. ODMR from a green c-plane InGaN/GaN MQW was studied to probe the method of carrier localisation in the QW. It was shown qualitatively that the ODMR results support current theories for carrier localisation mechanisms, but the noise on these measurements needs to be reduced to provide quantitative support.