As typically embodied, the present invention's RF cavity device comprises a rigid frame and plural flexible tiles. The frame includes walls of at least substantially uniform thicknesses that describe a hollow pillbox shape. The tiles are at least approximately equally thick, each tile being of at least substantially uniform thickness. Each tile includes a flexible metallic substrate and an HTS coating atop the substrate. The tiles are attached via their corresponding substrates to the inside wall surfaces of the frame so that their corresponding HTS coatings are interiorly exposed. The attached tiles flexibly conform to curved surface areas, are snugly set with narrow seams therebetween, and cover at least approximately the entirety of the frame's inside wall surfaces. A filler material is applied to the seams. The resultant tile configuration is characterized by at least approximate levelness of the exposed HTS coating surfaces and the filled seams.