An inspection apparatus (140) measures asymmetry or other property of target structures (T) formed by a lithographic process on a substrate. For a given set of illumination conditions, accuracy of said measurement is influenced strongly by process variations across the substrate and/or between substrates. The apparatus is arranged to collect radiation scattered by a plurality of structures under two or more variants of said illumination conditions (p1−, p1, p1+; λ1−, λ1, λ1+). A processing system (PU) is arranged to derive the measurement of said property using radiation collected under a different selection or combination of said variants for different ones of said structures. The variants may be for example in wavelength, or in angular distribution, or in any characteristic of the illumination conditions. Selection and/or combination of variants is made with reference to a signal quality (302, Q, A) observed in the different variants.