We evaluate the performance of thin-film silicon micromorph tandem solar cells deposited on transparent superstrates with embossed micrometer-scale 2-D gratings. Once coated with a thin conductive layer of hydrogenated indium oxide, the textured superstrates can be used as 2-D periodic single-texture front electrodes. Combining these almost loss-free front electrodes with a highly transparent, random self-textured zinc oxide layer (with a thickness 1 um) deposited by low-pressure chemical vapor deposition (LPCVD), we obtain double-texture transparent front electrodes. The potential of both single- and double-texture front electrodes is estimated by varying the illumination spectrum of the solar simulator, thereby assessing the maximum efficiency of the tandem cells under optimal current-matching conditions. Our results demonstrate the complementary roles of the 2-D gratings and the LPCVD-ZnO layers in double textures: Cell efficiencies as high as with our state-of-the-art 2.3-um-thick LPCVD-ZnO front electrode are obtained with significantly reduced ZnO layer thicknesses. Additionally, we show that equivalent efficiencies are also within reach with 2-D periodic single textures if the proper cell configuration is applied.