Theory of frame has been extended from Hilbert spaces to various spaces, specially, to Hilbert C *-modules. The paper introduces operator duals for frames with C *-valued bounds in Hilbert C *-modules. It is shown that operator duals for frames (*-frames) share several useful properties with ordinary duals. Some operator duals are constructed by a given operator dual or a given *-frame. Also, a characterization of all of operator duals for a given *-frame is obtained. Moreover, dilations of frames and their operator duals are studied. And, an application for frames and operator duals is suggested.