Wave energy is increasingly being seen as an alternative source of low-emissions power particularly for Australia, as Australia has abundant wave resources. This paper, using the performance characteristics of wave energy converters (WEC), resource measurements along Australia's southern coastline and global resource estimates, models projections of the future uptake of wave energy globally and in Australia. Globally, wave farms are projected to be installed up to a presumed maximum limit of 500 GW. In Australia there is more variability in the amount of wave farms installed, with differences across the different WEC. The outcome globally and in Australia depends on variations in the average power generated by the WEC and the carbon price path. In Australia, the majority of projected WEC installations are in the state of Victoria, which has relatively high demand and currently highly-emissions intensive sources of generation compared to states with better wave resources. When a dispatchable, or continuous power ability is added to wave energy's output the uptake of wave energy increases in Australia, in those states with the best resources. When the amount of wave energy extractable in any region is increased or decreased it has a large effect on output in Victoria in particular, which generates power from wave energy up to 30% of the total extractable resource under the dispatchable power scenario. Wave energy has the potential to make a significant contribution to electricity generation globally and in Australia.