Provided are methods and systems related to computer-assisted joint replacement surgery, and corresponding instrumentation systems. In one example, there is provided a system for guided surgery comprising: a sensor for coupling to a first bone to receive positional signals; a beacon for coupling to an object to provide the positional signals to the sensor, the object comprising one of a second bone and a surgical tool; a patient-specific jig (PSJ) for guiding a relative position of the sensor and the first bone during coupling to position the sensor in a predetermined pose in an anatomical coordinate frame; and an intra-operative computing unit in communication with the sensor, the intra-operative computing unit configured to calculate poses of the beacon with respect to the anatomical coordinate frame utilizing pre-operative data representing the PSJ and display positional information for the object in real time.