A numerical model of tsunami inundation, Delft3D, which has been validated for the 29 September 2009 tsunami in Tutuila, American Samoa, is used to better understand the impact of fringing coral reefs and embayments on tsunami wave heights, inundation distances, and velocities. The inundation model is used to explore the general conditions under which fringing reefs act as coastal buffers against incoming tsunamis. Of particular interest is the response of tsunamis to reefs of varying widths, depths, and roughness, as well as the effects of channels incised in the reef and the focusing effect of embayments. Model simulations for conditions similar to Tutuila, yet simplified to be uniform in the alongshore, suggest that for narrow reefs, less than about 200 m wide, the shoaling owing to shallow water depths over the fringing reef dominates, inducing greater wave heights onshore under some conditions and farther inundation inland. As the reef width increases, wave dissipation through bottom friction begins to dominate and the reef causes the tsunami wave heights to decrease and the tsunami to inundate less far inland. A sensitivity analysis suggests that coral reef roughness is important in determining the manner in which a fringing reef affects tsunami inundation. Smooth reefs are more likely to increase the onshore velocity within the tsunami compared to rough reefs. A larger velocity will likely result in an increased impact of the tsunami on structures and buildings. Simulations developed to explore 2D coastal morphology show that incised channels similar to those found around Tutuila, as well as coastal embayments, also affect tsunami inundation, allowing larger waves to penetrate farther inland. The largest effect is found for channels located within embayments, and for embayments that narrow landward. These simulations suggest that embayments that narrow landward, such as Fagafue Bay on the north side of Tutuila, and that have an incised deep channel, can cause a significant increase in tsunami wave heights, inundation distances, and velocities. Wide embayments, similar in size to Massacre Bay, induce some tsunami amplification, but not as much as for the narrowing embayment.