A method for producing a ceramic substrate material having a first layer and possibly a further layer is specified. The first layer comprises at least one first component made of a crystalline ceramic material and/or a glass material as a matrix and a second component made of a further crystalline ceramic material, which is provided in the matrix. An etching step is performed, mantle areas of the crystals and/or crystal agglomerates of the second component being etched selectively in the first layer to generate a cavity structure in the first layer. The present invention also relates to a corresponding ceramic substrate material, an antenna or an antenna array, and the use of the ceramic substrate material for an antenna or an antenna array.