This thesis presents the results of precise X-band electron paramagnetic resonance studies of zircon (ZrSiO4) and α-quartz (SiO2) single crystals at temperatures between 15 and 100 K, and the synthesis of the zircon crystals studied. Zircon crystals have been grown using the flux-growth technique, producing well-shaped crystals up to 4 mm in length. The technique was used to grow both doped and nominally undoped crystals. Dopants successfully incorporated into the zircon crystals were titanium, chromium, yttrium, aluminium and boron. Analysis of Ti4+ /Y3+ -doped zircon crystals revealed four defect centres new to the Canterbury research group. Two oxygenic hole centres have been analysed, one compensated by yttrium ([SiO4/Y]0), and the other by an unknown ion ([SiO4/M]n). A crystal-field spin-orbit coupling analysis of hole centres with a range of g values has shown that their anisotropy may be directly related to crystal-field splittings of orbital energy levels. A Ti3+ electron centre, Si(Ti3+), has been shown to be located in a silicon lattice position in contrast to an earlier-discovered Ti3+ centre in a zirconium lattice position, Zr(Ti3+). Another electron centre labelled H (g∥ = 1.9875, g⊥ = 1.9550) has been measured,but is not yet understood. A previously observed electron centre (Z) with effective g values of 1.9991 and 3.9118 has been shown to be a chromium ion in a silicon lattice position. A +3 oxidation state, and a large zero-field splitting has been inferred from an analysis of the effective g values. Two closely related boron centres have been observed in zircon crystals with relatively high boron doping, and have been interpreted as impurity electron centres in a zirconium lattice site. Both have almost identical g values gx = 1.969, gy = 1.981, gz = 1.969. One of the centres has the unusual point-group symmetry for defects in zircon of mm2 (C2v), which is explained by two adjacent ions along one of the zircon fourfold rotation-inversion axes. Two centres in a-quartz have been measured and analysed. One has been interpreted as a silicon-vacancy oxygenic-hole centre, [HLi2O4]0, compensated by one hydrogen and two lithium ions. The hyperfine matrices have been analysed with some success using three different methods to ascertain the locations of the compensating nuclei. The second centre is a previously reported hydrogen-compensated iron centre in a silicon lattice site, [FeO4/H]0α. A pseudo cube analysis has been carried out in order to confirm the location of the iron ion, but the results have been found inconclusive.