TM6:
To check the serial number of your Thermomix® TM6, simply open the Menu by touching the '3-lines' at the top left of the screen and then proceed to 'Settings' on the display. Lastly, scroll down and choose the option 'Thermomix® Version & Update' to get to the serial number.
TM5:
You can find it by going to the Menu> Help> About Thermomix
The serial number of all Thermomix models can also be found on the type plate, located on the lower housing of the machine.