A promising approach for upgrading the performance of an established low-bandgap solar technology without adding much cost is to deposit a high bandgap polycrystalline semiconductor on top to make a tandem solar cell. We use a transparent silver nanowire electrode on perovskite solar cells to achieve a semi-transparent device. We place the semi-transparent cell in a mechanically-stacked tandem configuration onto copper indium gallium diselenide (CIGS) and low-quality multicrystalline silicon (Si) to achieve solid-state polycrystalline tandem solar cells with a net improvement in efficiency over the bottom cell alone. This work paves the way for integrating perovskites into a low-cost and high-efficiency (>25%) tandem cell.