Recent calculations of particle acceleration in supernova remnants (SNRs) are used to estimate the associated γ-ray production. For source spectra which are power-laws in momentum (or rigidity) the production efficiency of γ-rays with energy Egamma_>100MeV is shown to be about a factor 2-3 lower than the value conventionally used for the interstellar medium and to depend only weakly on the spectral index of the power-law (in the range expected). Because the energy transferred to accelerated particles is rather tightly constrained by the total Galactic cosmic ray power, if SNRs are the main source of Galactic cosmic rays, this leads to an almost model-independent prediction of the SNR γ-ray luminosity in the band Egamma_>100MeV. A detailed discussion of instrumental sensitivities and backgrounds shows that detection of SNRs in the Egamma_>100MeV band with, for example, the Energetic Gamma Ray Experiment Telescope (EGRET) will be difficult, but should not be impossible. However, and significantly, the prospects look much better in the TeV band accessible to modern imaging atmospheric Cherenkov telescopes. It should be possible to detect SNRs out to distances of several kpc if the region of the ISM into which they are expanding has a high enough density (n>0.1cm^-3^) so that their γ-ray luminosity is high enough. Finally, it is pointed out that existing and planned air-shower arrays can place important limits on the extension of the accelerated particle spectra in SNRs to energies above 100TeV. In conjunction with spectral measurements in the TeV region and detections or upper limits in the 100MeV band this could provide a crucial test of current theories of particle acceleration in SNRs.