The amplification of coastal hazards such as distant-source tsunamis under future relative sea-level rise (RSLR) is poorly constrained. In southern California, the Alaska-Aleutian subduction zone has been identified as an earthquake source region of particular concern for a worst-case scenario distant-source tsunami. Here, we explore how RSLR over the next century will influence future maximum nearshore tsunami heights (MNTH) at the Ports of Los Angeles and Long Beach. Earthquake and tsunami modeling combined with local probabilistic RSLR projections show the increased potential for more frequent, relatively low magnitude earthquakes to produce distant-source tsunamis that exceed historically observed MNTH. By 2100, under RSLR projections for a high-emissions representative concentration pathway (RCP8.5), the earthquake magnitude required to produce >1 m MNTH falls from ~Mw9.1 (required today) to Mw8.0, a magnitude that is ~6.7 times more frequent along the Alaska-Aleutian subduction zone.