We study the effects of quenching in N=1 Super-Yang-Mills theory. While supersymmetry is broken, the Lagrangian acquires a new flavour U(1 |1) symmetry. The anomaly structure thus differs from the unquenched case. We derive the corresponding low-energy effective Lagrangian. As a consequence, we predict the mass splitting expected in numerical simulations for particles belonging to the lowest-lying supermultiplet. An estimate of the systematic error due to quenching follows.