Waves erode sea cliffs by various mechanisms, but the influence of wave power on bedrock coastal erosion has not been well quantified, making it difficult to predict how rocky coasts evolve in different environments. Volcanic ocean islands offer a unique opportunity to examine the influence of waves on bedrock coastal erosion because many islands have relatively homogeneous bedrock, well-constrained initial topography, and considerable differences in wave power between shorelines that face different directions and wave regimes. We used lava-flow ages and the morphology of coastal profiles on Maui, Kaho‘olawe, and the Big Island of Hawai‘i (USA) to estimate sea-cliff retreat rates at 11 sites that experience nearly eightfold differences in incident wave power. Using a range of possible sea-level histories that incorporate different trends of subsidence due to volcanic loading, we modeled the evolution of each coastal profile since its formation (12 ka to 1.4 Ma) to find the regionally consistent relative sea-level history and the site-specific sea-cliff retreat rates that best reproduce observed coastal profiles. We found a best-fit relative sea-level history prescribed by an effective elastic lithosphere thickness of 30 km, consistent with estimates from observations of total deflection beneath the Hawaiian Ridge. This suggests that coastal profiles may retain a decipherable record of sea-level change. Comparing the best-fit sea-cliff retreat rates to mean annual wave power at each site, which we calculated from 30 yr hindcast wave data, we found a positive relationship between wave power and sea-cliff erosion, consistent with theoretical predictions and measurements on unlithified coastal bluffs. These comparisons provide field evidence that bedrock coastal erosion scales with wave power, offering a basis for modeling rocky coast evolution in different wave climates.