The problem of resampling factor estimation as a means for tampering detection has been largely investigated. Most of the existing techniques rely on the analysis of cyclic correlations induced in the resampled signal. However, in this paper, a new direction is explored by addressing the same problem in terms of the set-membership estimation theory. The proposed technique constructs a model of the problem using available a priori knowledge and in consonance with a finite number of observations that comes from the resampled signal under study. With this information, the proposed technique is able to provide an estimate of the resampling factor applied to the original signal and, if required, an estimate of such signal and an estimate of the interpolation filter. The performance in terms of accuracy and MSE of the proposed approach is evaluated and comparative results with state-of-the-art methods are reported.