We explore the use of the inverse amplitude method for unitarization of scattering amplitudes to derive the existence and properties of possible new heavy states associated with perturbative extensions of the electroweak breaking sector of the Standard Model starting from the low-energy effective theory. We use a toy effective theory generated by integrating out a heavy singlet scalar and compare the pole mass and width of the unitarized amplitudes with those of the original model. Our results show that the inverse amplitude method reproduces correctly the singlet mass up to factors of O(1-3), but its width is overestimated.