Perovskite/silicon tandem solar cells allow to overcome the power conversion efficiency limit of market-dominating silicon solar cells. So far, various textured tandem devices were presented aiming at improved optical performance, but highest efficiencies were still realized on polished silicon wafer cells enabling superior perovskite layer properties. Here we present perovskite/silicon tandem solar cells with gentle periodic nanotextures which feature various advantages without compromising the material quality of solution-processed perovskite layers. Reflection losses are reduced in comparison to planar tandems and the devices are less sensitive upon deviations from optimum layer thicknesses. The nanotextures also enable excellent perovskite film formation and a greatly increased fabrication yield. The open-circuit voltage improved by about 15 mV due to enhanced electronic properties of the perovskite top cell. In addition, an optically advanced rear reflector with a dielectric buffer layer reduced parasitic absorption at near-infrared wavelengths. Altogether, the improvements enabled a certified power conversion efficiency of 29.80%.