Carbon-14 (14C) has been measured in groundwater for over half a century and remains a widely used tool for understanding groundwater flow systems. Ultimately, the usefulness of 14C as a groundwater tracer relies on the ability to distinguish between changes in concentration due to various chemical/physical processes (e.g. chemical reactions with solid carbonate material, conditions at the water table), and changes due to ageing along flow paths, the latter being most informative of groundwater flow conditions. To this end, a number of correction methodologies have been developed to account for chemical modifications in groundwater systems. In this paper, we implement two different single sample correction models, one for closed and one for open system carbonate dissolution in conjunction with a Markov chain Monte Carlo (MCMC) approach at two sites; the sedimentary Port Willunga Formation Aquifer in South Australia and a fractured rock aquifer in the Hamersley Basin, northwest Australia. For comparison, we include argon-39 (39Ar) data taken from some of the wells sampled and use a mixing envelope constraint in the MCMC procedure. We found that considering all of the errors associated with 14C correction resulted in a distribution of values to consider for groundwater dating procedures. When accounting for all parameters associated with single sample correction techniques, the associated error was 10 times greater than the analytical errors. Additionally, inclusion of the 39Ar data produced mixed results, with little improvement observed in the Port Willunga Aquifer (closed system correction), and a significant improvement observed at the Hamersley site (open system). This is most likely due to the mixing caused by long screens and the sensitivity of the open system correction model. Our results highlight the importance of considering all sources of error in groundwater dating studies.