  We consider elliptic variational inequalities generated by obstacle type
problems with thin obstacles. For this class of problems, we deduce estimates
of the distance (measured in terms of the natural energy norm) between the
exact solution and any function that satisfies the boundary condition and is
admissible with respect to the obstacle condition (i.e., it is valid for any
approximation regardless of the method by which it was found). Computation of
the estimates does not require knowledge of the exact solution and uses only
the problem data and an approximation. The estimates provide guaranteed upper
bounds of the error (error majorants) and vanish if and only if the
approximation coincides with the exact solution. In the last section, the
efficiency of error majorants is confirmed by an example, where the exact
solution is known.
