The relativistic charge carriers in monolayer graphene can be manipulated in manners akin to conventional optics (electron-optics): angle-dependent Klein tunneling collimates an electron beam (analogous to a laser), while a Veselago refraction process focuses it (analogous to an optical lens). Both processes have been previously investigated, but the collimation and focusing efficiency have been reported to be relatively low even in state-of-the-art ballistic pn-junction devices. These limitations prevented the realization of more advanced quantum devices based on electron-optical interference, while understanding of the underlying physics remains elusive. Here, we present a novel device architecture of a graphene microcavity defined by carefully-engineered local strain and electrostatic fields. We create a controlled electron-optic interference process at zero magnetic field as a consequence of consecutive Veselago refractions in the microcavity and provide direct experimental evidence through low-temperature electrical transport measurements. The experimentally observed first-, second-, and third-order interference peaks agree quantitatively with the Veselago physics in a microcavity. In addition, we demonstrate decoherence of the interference by an external magnetic field, as the cyclotron radius becomes comparable to the interference length scale. For its application in electron-optics, we utilize Veselago interference to localize uncollimated electrons and characterize its contribution in further improving collimation efficiency. Our work sheds new light on relativistic single-particle physics and provides important technical improvements toward next-generation quantum devices based on the coherent manipulation of electron momentum and trajectory.