Detection of a static eccentricity fault in rotating electrical machines is possible through several measurement techniques, such as shaft voltages and flux probes. A predictive maintenance approach typically requires that the condition monitoring technique is online, accurate, and able to detect incipient faults. This paper presents a study of the optimal measurement modality that leads to a minimal identification error of the static eccentricity in synchronous machines. The Cramer-Rao lower bound technique is implemented by taking into account both measurement and model uncertainties. Numerical results are obtained using a two-dimensional finite element model and is experimentally validated on a synchronous two-pole generator. Results indicate that shaft voltage measurements are better suited to the detection of static eccentricity.