So we chose an IC to use -> M24LR04E

We already know the antenna is supposed to be some sort of LC-resonant circuit. Checking the datasheet on the first page we see there is an internal tuning capacitance of ~27,5pF. The Frequency NFC works at is ~13,56MHz.

Easy calculation:

Lets check what LTSpice has to say:

Seems about right.

Next step is to get the antenna dimensions.
I already designed the PCB outline which gives me a maximum diameter.
Also the prototype will be manufactured by Aisler.

So we check the Aisler design rules for the maximum dimensions.

Input everything into a practical PCB coil calculator.
And let the Kicad-Coil addon draw something for us.
Put everything into a footprint.

And voilá:

Double checking the dimensions seem right.

Lets cross our fingers it will work.