We evaluate the application and investigate various formulae (and the associated parameter sensitivities) using the constant head well permeameter method to estimate field-saturated hydraulic conductivity (Kfs) in a previously glaciated temperate landscape in the Scottish Borders where shallow soils constrain the depth of augering. In finer-textured soils, the Glover equation provided Kfs estimates nearly twice those of the Richards equation. For this environment, we preferred the Glover equation with a correction factor for the effect of gravity, which does not include soil capillarity effects because: (1) the low depth to diameter ratio of the auger holes (AH) required in the shallow stratified soils of temperate glaciated environment needs a correction for gravity; (2) the persistently moist environment and the use of long pre-wetting times before measurements seem to reduce the effect of soil capillarity; (3) the Richards equation is dependent on accurate α* values, but the measured AH intersected soil horizon boundaries that had different soil structure and texture, causing difficulty in selecting the most appropriate α* value; (4) when comparing the different solutions to estimate Kfs using the constant-head well permeameter method against the AH method and ponded permeameter measurements, the Glover solution with a correction for gravity gave the best comparable result in fine-textured soil.