Methods were developed to characterize tapered capillaries as x-ray concentrators capable of forming spots of intense x-ray radiation with micrometer diameters. These tapered capillaries, with somewhat controlled tapers, were produced using a gravity-based capillary puller. A device was constructed to microscopically inspect these capillaries along two orthogonal axes in order to accurately measure the tapering and bending. Both monochromatic and white hard x rays were concentrated with a variety of tapered capillaries, and the subsequent gains in intensity (flux/area) ranging from 14 to 35 are reported. Using these unique x-ray concentrators, a simple high-powered x-ray fluorescence microscope was constructed and tested. We also found that hard x-ray beams could be successfully steered by bending the capillary tip with radii as small as 5 m. In addition, preliminary ray-tracing results obtained from a two-dimensional ray-tracing program are described.