The new exotic pentaquark resonances recently reported by LHCb in the J/ψ p channel are excellent candidates for photoproduction off a proton target. Such photoproduction experiments are a crucial test for confirming that these states are genuine resonances rather than a kinematical artifact. We focus on the interpretation of the heavier narrow state as a deuteronlike bound state of Σc and D∗, and employ vector dominance to estimate its production cross section. The relevant experiments can likely be performed in GlueX and CLAS12 detectors at JLAB which have the relevant photon energies and fluxes. We also perform a calculation for photoproduction of an analogous resonance in the bottomonium sector, predicted to exist in the ϒp channel.