Noting down a game of ZÈRTZ shouldn't cause too much trouble. The only difficulty is that you must take care not to lose track with the coordinates while the board shrinks. For that reason, it may be handy to draw a pattern of the board and assemble the rings on that pattern. To make it even more easy, you can already mark the spaces with their respective coordinates. That way taking notes of ZÈRTZ will become a piece of cake (in particular when comparing it with noting down a game of GIPF!).

 Board with 37 rings.

The board consist of 7 vertical rows, marked with the letters "a" to "g". Count the rings from the bottom upwards. Use small letters for the coordinates and capitals to indicate the colour of the marbles: W(hite), G(ray) and B(lack).

A. Placing a marble and removing a ring.
First note down the colour of the marble you choose to play with and the coordinate of the ring you put it onto. Next you put a comma, followed by the coordinate of the ring you remove.
For example: Wd4,d1
B. Capturing one or more marbles by jumping.
A capture must be marked with a small "x". That you note down first. Next you write down the coordinate of the ring with the marble you'll use to capture, followed by the letter that indicates the colour of the marble you capture, and next the coordinate of the ring where your move ends. If you can make a second capture, you go on with the letter of the second marble you jump over, followed by the coordinate of the ring where the marble lands, etc.
For example: x d1Gd3Wd5
C. Capturing one or more marbles by isolating.
Note down your move as described in A. above. If the ring you remove isolates one or more marbles, then you mark it with a small "x", followed by the colour(s) of the marble(s) you isolate and the coordinate(s) of the ring(s).
For example: Bd7,b2 x Wa1Wa2

 Board with 48 rings.