We discuss the possibility to study the in-medium changes of the properties of the omega meson in reactions on ordinary nuclei with elementary electromagnetic probes. We present a tree-level calculation of the elementary gamma p -> omega p process which is extended to describe also the photoproduction of medium-modified omega mesons in nuclear matter. Using a semi-classical transport approach we obtain results for e+e- and pi0 gamma photoproduction off heavy nuclei in the invariant mass range of the rho and omega mesons. Both reactions are also studied experimentally and are presently being analyzed at accelerator facilities in Bonn and at Jefferson Lab. We show that the in-medium signals expected can be as large as those obtained in heavy-ion reactions.