The microwave sensor produces an electrical output signal according to a position or displacement of a movable mechanical part (2), especially a valve needle in an injector valve for injecting fuel into an internal combustion engine. This position or displacement sensor includes a cavity resonator (40,70) provided with walls bounding a cavity (4,7) dimensioned for microwaves of a predetermined frequency and an antenna (8,14) for reception of the microwaves in the cavity. The end (3) of the movable mechanical part (2) protrudes into the cavity. A hybrid evaluating circuit (9) is connected with the antenna, which detects changes in the microwave radiation fed into and coupled out of the cavity, e.g. phase relationships, which depend on the position of the mechanical part (2), so that small position changes in very tight spaces are accurately determined.