Previously published calculations claim that gravitational waves propagate inside superconductors with a phase velocity reduction of ∼300 times and a wavenumber increase of ∼300 times. Subsequent claims that this result is not credible appear to be either not tenable or not complete. This result has major consequences for the design of instruments to generate and detect gravitational waves, in particular high-frequency gravitational waves (HFGWs) having wavelengths on the same order as the dimensions of typical superconductive components. It is generally assumed that in free space the velocity of an HFGW is the same as that of light and so the free space wavelength of an HFGW at 3 GHz will be ∼10 cm. Inside a superconductor, the corresponding 3 GHz HFGW wavelength will therefore be ∼300 μm. The present paper will discuss the technical consequences of this surprising result. In particular, such a large mismatch in HFGW propagation impedance inevitably results in large Fresnel reflections from superconductor-air interfaces. This will cause a number of design problems in equipment proposed for HFGW generation and detection. For example, the superconductor thickness used in HFGW detectors will be critical. It may also be possible with care to exploit the result to obtain HFGW resonators and focusing reflectors.