The EGR monitor can not be replaced, in that it is not a smog component. Emission monitors are internal self-tests which the Engine Control Unit performs to ensure a vehicle is not polluting and is running efficiently. The entire process of self-testing various emission control systems is called a Drive Cycle.
In this particular case we'd recommend a smog check repair station look-up your particular vehicle's OBD requirements to ensure that the vehicle has no known EGR monitor setting problems identified by the California Air Resource Board; in which case the smog technician should be able to bypass the monitor(s) portion of the smog inspection. It should be noted however, that in most cases, the BAR (Bureau of Automotive Repairs) has already download information into individual smog stations' smog machines with information automatically bypassing the particular monitor(s) portion of the smog inspection for which vehicles have shown difficulty setting/passing. In other words, in most cases, when an emission monitor setting problem has been identified by BAR or CARB, the smog machine is already programmed to bypass the testing of said monitor.
After a smog technician ensures your vehicle does not fall withing the bypass criteria, he/she should look up the exact drive cycle requirement for your vehicle's EGR monitor and perform the drive cycle on a dynamometer (for safety, as opposed to driving on city/highway) and complete the drive cycle as close to the require parameters as possible. If still the EGR monitor (or any other monitor for that matter) is unable to complete, the technician must follow the required criteria for the drive cycle to run and ensure the required criteria is being met; whether that be driving speed, time, necessary emission sensor input values, and/or monitors which need to complete prior to the next monitor running.
Start with making sure your vehicle has no known EGR monitor setting issues identified by the BAR and CARB, and next get in to hands-on diagnosis of what is causing the monitor to either not run or not complete. Since the check engine light is not on, we can be confident the ECU has not found any specific emission component failure. The job will now be for a technician to test input/output values of the engine emission sensors and solenoids for proper voltage and parameters are required by the engine manufacturer.