The current status and issues regarding positron dosimetry in nuclear medicine are summarized. The suitability of the UKHSA extremity and eye beta-gamma personal thermoluminescence dosemeters are then considered. Monte Carlo modelling is performed to determine their responses and derive sets of calibration factors, along with Hp(0.07) and Hp(3) conversion coefficients, for carbon 11, nitrogen 13, oxygen 15, fluorine 18 and gallium 68 sources, which are commonly used in PET-CT; data for these isotopes is assumed extrapolatable to other positron sources. It is found that the dosemeters are adequate for assessing exposures to PET radionuclides, even if their routine calibrations to caesium 137 were maintained. An idealized set of measurements representing gallium 68 exposure scenarios is then described, including reproducible mock-ups of individuals manipulating vials and syringes. Finally, a short case-study is presented that explores occupational doses during routine clinical use of gallium 68. The extremity dosemeter results demonstrated significant variations dependent upon the exposure conditions, with some seen to be comparatively large; whole-body and eye dose rates per activity were found to be lower. The importance of routine dose monitoring of workers is emphasized, with the need for a longer-termed follow-up study demonstrated.