Efficient light management in monolithic perovskite/silicon tandem solar cells is one of the prerequisites for achieving high power conversion efficiencies (PCEs). Textured silicon wafers can be utilized for light management, however, this is typically not compatible with perovskite solution processing. Here, we instead employ a textured light management (LM) foil on the front-side of a tandem solar cell processed on a wafer with a planar front-side and textured back-side. This way the PCE of monolithic, 2-terminal perovskite/silicon-heterojunction tandem solar cells is significantly improved from 23.4% to 25.5%. Furthermore, we validate an advanced numerical model for our fabricated device and use it to optically optimize a number of device designs with textures at different interfaces with respect to the PCE and energy yield. These simulations predict a slightly lower optimal bandgap of the perovskite top cell in a textured device as compared to a flat one and demonstrate strong interdependency between the bandgap and the texture position in the monolithic stack. We estimate the PCE potential for the best performing both-side textured device to be 32.5% for a perovskite bandgap of 1.66 eV. Furthermore, the results show that under perpendicular illumination conditions, for optimized designs, the LM foil on top of the cell performs only slightly better than a flat anti-reflective coating. However, under diffuse illumination, the benefits of the LM foil are much greater. Finally, we calculate the energy yield for the different device designs, based on true weather data for three different locations throughout the year, taking direct as well as diffuse illumination fully into account. The results further confirm the benefits of front-side texture, even more for BIPV applications. Overall, devices built on a both-side textured silicon wafer perform best. However, we show that devices with textured LM foils on the cell's front-side are a highly efficient alternative.