I'm gonna be honest, I don't think it's very likely that the necklace is real and even if it is, Princess Michael wouldn't own it, it would probably just be on loan.
The reason I say this is because a collar like that would be worth hundreds of thousands if not millions of pounds. As much as Prince Michael tries to preserve his royal legacy, he's not on the Civil List and I doubt he could afford to hang onto a piece like this.
As for the Emerald brooch, I would guess that it was loan for that particular event. It looks like an Indian inspired piece and it was worn at a party to celebrate the publication of 'Made for Maharajas' by Dr Amin Jaffer.