A rotary machine includes a stator and a rotor configured to rotate with respect to the stator. The rotor is arranged with the stator at a rotor-stator interface and defines a rotor face. Further, the rotary machine includes a seal assembly at the rotor-stator interface. The seal assembly includes at least one seal and a groove formed into the rotor at the rotor-stator interface. In addition, the seal assembly includes a removable insert positioned within the groove of the seal assembly and defining at least a portion of the rotor face. As such, during operation of the rotary machine, if the rotor and the stator make undesirable contact at the rotor-stator interface, the removable insert becomes damaged to prevent damage from occurring to the rotor and the stator.