In three different phase-separated binary liquid mixtures we have observed stationary capillary rises in which the meniscus curvature is inconsistent with the sign of the rise. This ‘‘inverted-meniscus’’ configuration occurs within approximately 50 mK of the mixture’s critical temperature and shows no sign of decay after much longer than the characteristic time for relaxation. We also report experiments showing that perturbation of the wetting layer inside the capillary tube can dramatically affect the capillary rise. This motivates three scenarios in which the behavior of the wetting layer foils an equilibrium capillary rise measurement of the contact angle and produces an inverted meniscus.