A method is described for the measurement of characteristics of pickup electrodes (PUE) for monitoring coordinates of an accelerator beam. A new representation is discussed for determining the coordinates of the center of charge for the entire PUE aperture. A few prototypes of PUE's to be installed in the AGS were tested and the results show that nonlinear deviations are at least 1 mm/25 mm. The method of measurement has a resolution of at least 0.1 mm/25 mm; it can therefore be used for (a) the design of high quality PUE's and (b) calibration of PUE's as installed in the accelerator in order to increase the usable aperture and the accuracy of beam coordinate monitoring.