Strain-gradient plasticity has become well established as an approach to modelling size-dependent phenomena at the meso- and microscales. The various gradient theories are characterized by the incorporation of one or more length scales that allow size-dependent behaviour to be captured. These approaches have sought to model strengthening behaviour, that is, an increase in initial yield with length scale, and hardening behaviour, which manifests as an increase in hardening with length scale. This presentation is concerned with determining the threshold of elastic behaviour in situations of strengthening behaviour, for which a dissipative strain-gradient theory is relevant. For such models yield cannot be determined locally, analogously to conventional rigid-plasticity. As in the latter case the techniques of limit analysis, suitably generalized to the gradient problem, are used to establish lower and upper bounds to the threshold. These bounds are compared with results in the literature for classical micro-scale experiments, for example, on torsion and bending.