The atomic masses of $^{74}\mathrm{Ge}$, $^{74}\mathrm{Se}$, $^{76}\mathrm{Ge}$, and $^{76}\mathrm{Se}$ have been determined from cyclotron frequency ratios of pairs of ions simultaneously trapped in a cryogenic Penning trap. Allowing for cancellation of systematic errors in the mass differences between isobars, we determine the $Q$ value for double-electron capture of $^{74}\mathrm{Se}$ to be 1209.240(7) keV, and the $Q$ value for double-electron emission of $^{76}\mathrm{Ge}$ to be 2039.061(7) keV. The new ${Q}_{2\mathrm{EC}}$ value for $^{74}\mathrm{Se}$ precludes a large resonant enhancement for neutrinoless double-electron capture.