The boundary conditions appropriate to the finite Larmor radius (FLR) wave equations that describe wave propagation in the ion cyclotron and lower hybrid frequency ranges in plasmas have been derived. These equations possess three independent solutions, one more than the Maxwell equations in vacuum; to establish the additional condition at a plasma-boundary interface needed to define unambiguously the causal solution in the plasma, it is shown that HF diamagnetic currents (proportional to the gradients of the equilibrium plasma parameters) remain finite in the limit in which the thickness of the plasma-vacuum transition is assumed to be negligible compared with the perpendicular wavelength of the incident waves. The discontinuity of the compressional component of the wave field due to these HF surface currents can be expressed in terms of the FLR contributions to the coefficients of the wave equations, so that the FLR boundary conditions can be formulated in a fully explicit manner. It is also shown that these conditions guarantee the continuity of the power flux through the plasma surface. These boundary conditions have been used to obtain analytic expressions for the surface impedance matrix of a plasma in the FLR approximation, assuming that the WKB solutions to the wave equations can be used near the plasma edge. These analytic results can be used to check numerical solutions of the wave equations against a known case, and to speed up the solution of antenna coupling problems in large plasmas