We discretise a tangential tensor field equation using a surface-finite element approach with a penalisation term to ensure almost tangentiality. It is natural to measure the quality of such a discretisation intrinsically, i.e., to examine the tangential convergence behaviour in contrast to the normal behaviour. We show optimal order convergence with respect to the tangential quantities in particular for an isogeometric penalisation term that is based only on the geometric information of the discrete surface.