Microscale pyramids of silicon solar cells are often considered incompatible with solution-processed perovskite films. Thus, solution processing has mainly been used with submicron pyramids that are buried under thick perovskite films with flattened front surfaces. Yet, while this modification simplifies the fabrication process, it compromises optical performance compared to conformal perovskite films (e.g., obtained by vapor processing). Here, we show that protrusion-free perovskite films can be formed on random pyramids much higher than the film thickness by tailoring the film thickness to match the pyramids' height profile, notably without modifying the pyramid facets. Accordingly, we demonstrate perovskite cells spin-coated on over 2 mu m-high random pyramids with electronic performance comparable to those fabricated on flat substrates, and proof-of-concept perovskite-silicon tandem devices with efficiencies reaching 33%. Finally, we show that the undulated films with enhanced conformality enable optical performance superior to flat surfaces, especially upon encapsulation, most relevant to outdoor applications.