Apparatus and methods are disclosed for detecting and measuring a tool-induced shift in a microlithography apparatus (“stepper”). The apparatus and methods are set forth in the context of microlithography apparatus that include a wafer stage and a holding member to which the wafer is mounted for exposure. The holding member can include, for example, a wafer table and wafer chuck, wherein the wafer table desirably includes a respective movable mirror for each of X- and Y-directions of movement. The holding member is rotatable, relative to the wafer stage, from a first rotational position to a second rotational position, which can be angularly displaced, e.g., 90° and/or 180° from each other. At each of the first and second rotational positions, a respective location of an alignment feature on the holding member (e.g., on the substrate, wafer chuck, or wafer table) is determined. The respective locations at the first and second rotational positions are compared, and a corresponding tool-induced shift is determined from a detected difference between the respective locations. Rotation of the holding member desirably is effected using a rotary actuator.