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.