The phase picked up by a graphene plasmon upon scattering by an abrupt edge is commonly assumed to be -π. Here, it is demonstrated that for high plasmon momenta this reflection phase is ≈-3π/4, virtually independent on either chemical potential, wavelength, or dielectric substrate. This nontrivial phase arises from a complex excitation of highly evanescent modes close to the edge, which are required to satisfy the continuity of electric and magnetic fields. A similar result for the reflection phase is expected for other two-dimensional systems supporting highly confined plasmons (very thin metal films, topological insulators, transition polaritonic layers, etc.). The knowledge of the reflection phase, combined with the phase picked up by the plasmon upon propagation, allows for the estimation of resonator properties from the dispersion relation of plasmons in the infinite monolayer. © 2014 American Physical Society.