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166.6-MHz quarter-wave β=1 superconducting cavities have been adopted for the High Energy Photon Source, a 6-GeV diffraction-limited synchrotron light source currently under construction. A large helium jacket was required to accommodate the enlarged cavity beam pipe for the heavy damping of higher-order modes; the original electric-probe pickup thus becomes inevitably long with unfavorable mechanical properties. Relocated to an existing high-pressure-rinsing port, a magnetic-loop pickup was designed, characterized by low radio-frequency and cryogenic losses and being multipacting-free and insensi-tive to manufacturing and assembly tolerances. The con-sequent removal of the original pickup port from the cavity largely simplified the helium jacket fabrication and may also reduce cavity contamination. This paper presents a comprehensive design of a low-loss magnetic-coupling pickup for quarter-wave β=1 superconducting cavities. The design can also be applied to other non-elliptical structures.