A method is offered for orthogonal Procrustes rotation of two or more matrices with missing values, and an extension to Generalized Procrustes Analysis is given. The method is based on the idea that missing values, in arbitrary places, can be replaced by optimal values according to the least squares criterion. Commandeur has offered a method of orthogonal Procrustes rotation and Generalized Procrustes Analysis for the case where entire rows of the data matrices are missing. It is proved that our method yields essentially the same results as Commandeur's method, in that case. A simulation study for Procrustes rotation is described in which complete columns of matrices, derived from a common underlying structure, are deleted, and either replaced by zeros or estimated on the basis of the newly proposed method. In those conditions where the underlying structure can adequately be disentangled from the error, our method appears to recover the underlying structure more accurately than when the missing columns are replaced by zeros.