The MICARDO 2.1 driver supports Estonian ID cards.
It works with Estonian ID cards and OpenSC is the official software used in Estonia for these cards (on Linux, Mac OS X and for PKCS#11 in Mozillas on Windows).
For more information see the EstonianEid page.
MICARDO driver also has code to support German BMI / D-trust cards, but the functioning of those cards has not been tested for a long time.
The card manual is available in the attachment (but not officially distributed otherwise).