We study the behaviour of the information matrix (IM) test when maximum likelihood estimators are replaced with robust estimators. The latter may unmask outliers and hence improve the power of the test. We investigate in detail the local asymptotic power of the IM test in the normal model, for various estimators and under a range of local alternatives. These local alternatives include contamination neighbourhoods, Student's t (with degrees of freedom approaching infinity), skewness, and a tilted normal. Simulation studies for fixed alternatives confirm that in many cases the use of robust estimators substantially increases the power of the IM test.