Currently, you can prove ownership of coins by signing with
the private key of an address where coins are stored.
Is there a ZKP (Zero Knowledge Proof) way of demonstrating
that you own at least X BTC ?
That'd be a killer feature for credit-worthiness type applications
of bitcoin.
I don't think this is possible at all. To prove it you would always need to show something that ultimately links whatever that is to you address. And if you present something that cannot be linked to the address it's pointless. I don't know, I think it doesn't make much sense.