Perovskites with bandgaps between 1.7 and 1.8 eV are optimal for tandem configurations with crystalline silicon (c-Si) because they facilitate efficient harvest of solar energy. In that respect, achieving a high open-circuit voltage (V-OC) in such wide-bandgap perovskite solar cells is crucial for a high overall power conversion efficiency (PCE). Here, we provide key insights into the factors affecting the V-OC in wide-bandgap perovskite solar cells. We show that the influence of the hole transport layer (HTL) on V-OC is not simply through its ionization potential but mainly through the quality of the perovskite-HTL interface. With effective interface passivation, we demonstrate perovskite solar cells with a bandgap of 1.72 eV that exhibit a V-OC of 1.22 V. Furthermore, by combining the high-V-OC perovskite solar cell with a c-Si solar cell, we demonstrate a perovskite-Si four-terminal tandem solar cell with a PCE of 27.1%, exceeding the record PCE of single-junction Si solar cells.