The serial number for the UMIK-1 can usually be found on a sticker stuck on the microphone body. In case it is missing, you can always go back to the packaging box and the serial number should be available on the side of the box.
An alternative would be to open an old REW mdat file where you would have hopefully used the calibration file back then. If so, you would be able to find the calibration file number as shown below.
If you are still not able to find the serial number in both places and you purchased your UMIK-1 from miniDSP.com, we "might" be able to recover the SN for you based on our database providing it's not too old. Please contact our team for further support if we can help.