Power supply filtering RCL-filter vs alternatives (for LF-RFID driver)
the antenna driver has a maximum at ~250mA which is well below the 4A rating of the inductor. Can a smaller inductor be chosen?


A smaller inductor will almost certainly have a higher ESR. This will cause a higher DC voltage drop through the filter.

If you can accept that limitation, you can probably use a smaller inductor.

You should also consider whether that Schottky diode is there for a reason or not. If there is some expected reverse polarity event for it to protect the load against, you will need to be sure the inductor won't be blown out when that event occurs.


  I think the I_RMS rating is only relevant for maximum power handling and doesn't take into account effects of saturation.


Depending on the inductor design, the current limitation might be due to saturation, or it might be due to resistive loss. A good datasheet will tell you which. On the other hand, not all magnetics vendors provide highly detailed datasheets.


  Is there a better/smaller/more elegant way to achieve comparable or better filtering between, let's say 200-20kHz?


You might consider using two (possibly lower-valued) inductors with capacitors in between to make a two-section filter instead of this one-section filter. That will get you 40 dB/decade roll-off rather than 20-dB per decade.  Whether the overall performance is better for your application (and whether it's worth the increased cost and/or board area) is up to you to evaluate.