This paper is devoted to an analysis of vortex-nucleationfor a Ginzburg-Landau functional withdiscontinuous constraint. This functional has been proposedas a model for vortex-pinning, and usuallyaccounts for the energyresulting from the interface of two superconductors. Thecritical applied magnetic field for vortex nucleation is estimated inthe London singular limit,and as a by-product, results concerning vortex-pinning andboundary conditions on the interface are obtained.