In this paper, we discuss the accuracy of aquifer transmissivity (T) and storativity (S) values, obtained through the processing of hourly and 5-min groundwater level data, regularly and accurately recorded by automated stations. In particular, we discuss the role of the selection of (a) the initial undisturbed hydraulic head level, which might be influenced by prior pumping cycles, and (b) the exact time of start or shutdown of the pump, which might not be exactly recorded. Furthermore, the accuracy of T and S values based on sparse measurements is also examined. The Cooper–Jacob method and the recovery test method have been applied to obtain both T and S, and T values, respectively. Groundwater level measurements at Moudania aquifer, Chalkidiki, Greece, are used as an illustrative example. Our main conclusions are (a) assuming that pumping starts earlier than it actually does, leads to the underestimation of T and the overestimation of S, (b) transmissivity might be overestimated if the residual drawdown, due to previous pumping cycles, is substantial, (c) in recovery tests, the deviation of the straight line that fits the experimental points from the point (1,0) is an indication of residual drawdown, and (d) sparse measurements can offer reasonable estimates.