A clearance sensing system for a rotating machine includes a plurality of sensor probes disposed within a stationary shroud of the rotating machine. Each of the plurality of sensor probes is adapted to measure a parameter indicative of an axial and a radial displacement of a rotating component within the shroud and to produce a signal that corresponds to the parameter. In certain embodiments, this parameter may include a capacitance between the rotating component and the sensor probe. The clearance sensing system further includes a circuit that receives the signal from each of the plurality of sensor probes and determines (a) the axial displacement of the rotating component within the shroud and (b) a radial displacement of the rotating component relative to the shroud.