<i>Micro-appearance models</i> explicitly model the interaction of light with microgeometry at the fiber scale to produce realistic appearance. To effectively match them to real fabrics, we introduce a new appearance matching framework to determine their parameters. Given a micro-appearance model and photographs of the fabric under many different lighting conditions, we optimize for parameters that best match the photographs using a method based on calculating derivatives during rendering. This highly applicable framework, we believe, is a useful research tool because it simplifies development and testing of new models. Using the framework, we systematically compare several types of micro-appearance models. We acquired computed microtomography (micro CT) scans of several fabrics, photographed the fabrics under many viewing/illumination conditions, and matched several appearance models to this data. We compare a new fiber-based light scattering model to the previously used microflake model. We also compare representing cloth microgeometry using volumes derived directly from the micro CT data to using explicit fibers reconstructed from the volumes. From our comparisons, we make the following conclusions: (1) given a fiber-based scattering model, volume- and fiber-based microgeometry representations are capable of very similar quality, and (2) using a fiber-specific scattering model is crucial to good results as it achieves considerably higher accuracy than prior work.