[EvanAnderson]

Presumably you'll be using it with a browser. I'm sorry that I didn't clarify that assumption in my first response.

I don't know about Estonia in particular but I'm guessing "$SOME_GOVERNMENT's interfaces" for most places is going to be HTTPS.

So, with that in mind, I've used a Nitrokey HSM and a Taglio PIVKey with Firefox on Linux using the OpenSC tools PKCS 11 module. I would suspect any smart card supported by OpenSC will work fine in Firefox.

From my reading, OpenSC is being distributed by the government of Estonia, so I suspect using it in a browser that supports PKCS 11 modules compatible with OpenSC on a Linux PC would work fine.