Magnetic heterostructures consisting of single-crystal yttrium iron garnet (YIG) films coated with platinum are widely used in spin-wave experiments related to spintronic phenomena such as the spin-transfer-torque, spin-Hall, and spin-Seebeck effects. However, spin waves in YIG/Pt bilayers experience much stronger attenuation than in bare YIG films. For micrometer-thick YIG films, this effect is caused by microwave eddy currents in the Pt layer. This paper reports that by employing an excitation configuration in which the YIG film faces the metal plate of the microstrip antenna structure, the eddy currents in Pt are shunted and the transmission of the Damon-Eschbach surface spin wave is greatly improved. The reduction in spin-wave attenuation persists even when the Pt coating is separated from the ground plate by a thin dielectric layer. This makes the proposed excitation configuration suitable for injection of an electric current into the Pt layer and thus for application in spintronics devices. The theoretical analysis carried out within the framework of the electrodynamic approach reveals how the platinum nanolayer and the nearby highly conductive metal plate affect the group velocity and the lifetime of the Damon-Eshbach surface wave and how these two wavelength-dependent quantities determine the transmission characteristics of the spin-wave device.