The selection of statistical methods that can operate even on ill-conditioned problems, providing accurate estimation and supporting general inference tasks, is a central need in several applications in different domains. In this setting, two major approaches are the methods from the bridge estimation family, such as ridge regression, and the entropy-based methods, such as generalized maximum entropy estimation. Regarding these two methods, on the one hand, the appropriate choice of the shrinkage parameter in ridge regression is not always an easy task, and, on the other hand, the choice of supports for the parameters of the model is a usual difficulty with the generalized maximum entropy estimator. The RidGME estimator proposed in this work, using generalized maximum entropy with supports defined with information from the ridge trace, mitigates the weaknesses of both methodologies, revealing itself as an alternative to ridge regression on ill-conditioned models. The results from an empirical application reveal that the RidGME estimator is competitive with the best optimal choice of ridge estimators and outperforms the ordinary least squares estimator in a cross-validation root mean squared error sense. Its implementation is illustrated, and computational codes are made available to practitioners.