We point out that photon regeneration-experiments that search for the axion, or axion-like particles, may be resonantly enhanced by employing matched Fabry-Perot optical cavities encompassing both the axion production and conversion magnetic field regions. Compared to a simple photon regeneration experiment, which uses the laser in a single-pass geometry, this technique can result in a gain in rate of order ${\cal F}^2$, where ${\cal F}$ is the finesse of the cavities. This gain could feasibly be $10^{(10-12)}$, corresponding to an improvement in sensitivity in the axion-photon coupling, $g_{aγγ}$ , of order ${\cal F}^{1/2} ∼ 10^{(2.5-3)}$, permitting a practical purely laboratory search to probe axion-photon couplings not previously excluded by stellar evolution limits, or solar axion searches. ; Comment: 4 pages, 2 figures