Cryogenic energy-dispersive X-ray detectors are being developed because of their superior energy resolution (10 eV FWHM for keV X-rays) compared to that achieved in semiconductor energy-dispersive spectrometry (EDS) systems. So far, their range of application is limited because of their comparably small size and low count rate. We present data on the development of superconducting tunnel junction (STJ) detector arrays to address both of these issues. A single STJ detector has a resolution of around 10 eV below 1 keV and can be operated at count rates of the order 10,000 counts/sec. We show that the simultaneous operation of several STJ detectors does not dimish their energy resolution significantly, and it increases the detector area and the maximum count rate by a factor given by the total number of independent channels.