A mirror for a piezoelectric resonator consisting of alternately arranged layers of high and low acoustic impedance is manufactured by at first producing a first layer on which a second layer is produced, so that the second layer partially covers the first layer. Then, a planarization layer is applied on the first layer and on the second layer. Subsequently, a portion of the second layer is exposed by structuring the planarization layer, wherein the portion is associated with an active region of the piezoelectric resonator. Finally, the resulting structure is planarized by removing the portions of the planarization layer remaining outside the portion.