A superconducting tunnel junction (STJ) in combination with a superconducting absorber of radiation may function as a highly resolving x-ray spectrometer. Electronic excitations, or quasiparticles, are created when a superconductor absorbs an x ray and are detected as an excess tunnel current through the junction. The number of quasiparticles created and the magnitude of the excess current is proportional to the energy of the absorbed x ray. This is similar to existing semiconductor-based spectrometers that measure electron-hole pairs, but with 1000 times more excitations. The energy measurement therefore can be up to 30 times more precise with a superconducting detector than with a semiconductor detector. This work describes the development and testing of an STJ spectrometer design for x-ray fluorescence applications. First, the basic principles of the STJ spectrometer are explained. This is followed by detailed simulations of the variance in the number of quasiparticles produced by absorption of an x ray. This variance is inherent in the detector and establishes an upper limit on the resolving power of the spectrometer. These simulations include effects due to the materials used in the spectrometer and to the multilayer structure of the device. Next, the spectrometer is characterized as functions of operating …