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 (VOC) 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 VOC in wide-bandgap perovskite solar cells. We show that the influence of the hole transport layer (HTL) on VOC 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 VOC of 1.22 V. Furthermore, by combining the high-VOC 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.