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We present novel approaches to electromagnetic design of high-temperature superconducting (HTS) quarter-wave parallel coupled-line microstrip filters. The desired narrow bandwidths (less than 2%) coupled with the large dielectric constant of substrate materials used in the HTS technology (E, = 24) make the design problems difficult to treat accurately for many traditional microwave circuit design software packages with analytical/empirical models. We have successfully performed an HTS filter design with accurate electromagnetic field simulations. We discuss problems related to electromagnetic design of such filters. We describe a look-up table method and a powerful space mapping optimization technique, which dramatically reduce the CPU time needed in the design process. Finally, we address the issue of improved modeling of the HTS filter using analytical/empirical models.