The application of atom probe tomography to the study of minerals is a rapidly growing area. Picosecond-pulsed, ultraviolet laser (UV-355 nm) assisted atom probe tomography has been used to analyze trace element mobility within dislocations and low-angle boundaries in plastically deformed specimens of the nonconductive mineral zircon (ZrSiO4), a key material to date the earth’s geological events. Here we discuss important experimental aspects inherent in the atom probe tomography investigation of this important mineral, providing insights into the challenges in atom probe tomography characterization of minerals as a whole. We studied the influence of atom probe tomography analysis parameters on features of the mass spectra, such as the thermal tail, as well as the overall data quality. Three zircon samples with different uranium and lead content were analyzed, and particular attention was paid to ion identification in the mass spectra and detection limits of the key trace elements, lead and uranium. We also discuss the correlative use of electron backscattered diffraction in a scanning electron microscope to map the deformation in the zircon grains, and the combined use of transmission Kikuchi diffraction and focused ion beam sample preparation to assist preparation of the final atom probe tip.