Using density-functional theory, we compute the optical and static dielectric constants for a set of Zr silicates modeled by various SiO2 crystals, with Zr atoms substitutional to Si, and by an amorphous structure. We then derive a microscopic scheme that relates the dielectric constants to structural units centered on Si and Zr atoms through the definition of characteristic parameters. Applied to amorphous (ZrO2)(x)(SiO2)(1-x), these schemes describe the observed dependence of the dielectric constants on the Zr concentration and highlight the role of ZrO6 units.