In recent years, one of the questions about modified binders has been the durability of their improved performance throughout their service life. Aging properties of modified binders in various frequency and temperature ranges depend on the class and concentration of the modifiers as well as the binder type. The aging characteristics have been evaluated in several ways, but the use of master curve models for modified binders has received little attention because of the lack of appropriate models with an easily manageable number of parameters. A recently developed mathematical model, Double Logistic (DL), can be used to characterize the master curves of modified binders. For the investigation of the rheological properties of aged and unaged modified binders, two modifiers, styrene–butadiene–styrene and ground tire rubber, were selected. Two binder types were selected to evaluate the binder dependency of the results. All modified binders were subjected to short- and long-term aging conditions in the laboratory. Then the rheological master curves of the complex modulus and phase angle of all the binders in various aging conditions were generated and fitted by the DL model. The model correctly predicted the phase angle plateau values and other irregularities for many polymer-modified binders in several aging conditions in this research. In addition, the DL model captured aging behaviors, such as hardening or softening, more elastic or viscous response, and lower or higher temperature susceptibility of the neat and polymer modified binders at various temperature and frequency ranges.