It is shown that complications in currently used optical measurements for wetting and flow resistance over edges can be circumvented by surface tension force measurements. These forces are measured by employing a modified Wilhelmy plate testing technique in which a plate with rectangular holes is immersed. The forces measured during immersion and emersion are subdivided into mass, buoyancy, and surface tension related parts, where the flow resistance when the meniscus passes horizontal faces and edges of the plate receives particular attention. Combining this experimental method with wetting theory, we show that we can predict and measure the full force curve for meniscus shape transitions over edge geometries under quasi-static conditions. Moreover, wetting effects directly linked to surface defects can be detected qualitatively. We also point to the speed-dependent rupture of metastable films formed during emersion. The measurement method designed is most relevant in cases where optical methods cannot be used.