C-lines in vector electromagnetic waves are analogues of the more familiar optical vortices found in the complex scalar waves usually used to describe light. The centroid of a laser beam is shifted on reflection by the well-known Goos–Hänchen and Imbert–Fedorov effects, but if it carries a C-line two separate C-lines appear in the reflected beam, both of which are shifted, their shifts being unrelated to the well-known shift of the beam centroid. An experiment is described that tests the theoretical predictions for the shifts of the C-lines perpendicular to the plane of incidence. It used internal reflection in a glass prism close to the critical angle to enhance the effect. In a simple situation like this, two recently published independent theories of C-line reflection are both applicable and it is shown that their predictions are identical. Our measured differences in the shifts of the two reflected C-lines confirm both theories. Remarkably, the measurable C-line shifts are much larger (hundreds of micrometers) than traditional beam-shift displacements. Theoretically, the difference is infinite at the critical angle itself with a change of sign.