In this paper we describe the analysis of ceramic artifacts with a new type of three dimensional x-ray microscopy which can have micron spatial resolution. The x-ray microscopy is based on a microtomographic technique which reconstructs the three dimensional structure of millimeter sized specimens from high resolution digital radiographs of the specimenstaken from several hundred different view angles. When the high resolution radiographs are taken with a monoenergetic x-ray beam from a synchrotron source, each volume element (voxel) in the reconstructed data set is quantitatively the x-ray opacity of the equivalentvolume in the specimen. Typical reconstructed data sets contain more than 106 voxels and are rendered using computer visualization techniques. Specimens can be nondestructively analyzed so long as they are small enough to fit into the area of the x-ray beam imaged by the detector. We have applied x-ray microtomographic analysis both to a shardspecimen taken from a Jun bowl and to a modern ash glaze and show examples of the structure of glazes on these ceramics; interfaces between the glaze and underlying ceramic bodies; and the porosity of ceramic bodies.