Zurich 40 Batzen 1813 & Papal Medal 1684

Both appear to be cast fakes. Look on the edge of the coins for a line where the two mold halves met. They may also have been sanded to remove the mold lines, but there should still be tell-tale indications of same.

I don't have sufficient experience or skill to authenticate these from screen pictures, so I will say innocent until still to be proved otherwise.
It is worth noting that centrifugal pressure cast fakes can be made well enough, to have the potential to deceive people like me.

From the pictures, the surfaces suggest that they may have a greasy feel, suggesting pressure cast fake. Pressure cast fakes often show a high level of minute detail, often with no evidence of casting bubbles; that is why pressure casting is used.

A 'gut' feeling still leaves sufficient doubt in my mind, enough to take them to an experienced professional, who can examine them in hand, with a 10x loupe.

I think Edge pictures would be a deal breaker in this case. I believe I have seen similar fakes in the past, White metal, the weight should be off.

Well, the 2nd coin (the piastra) looks a bit odd, but these were often used as jewellery, therefore what one perceives as casting marks could be just heating damage.

The first coin (the swiss 40 batzen) appears polished, but not fake.

Even if authentic, the slabbing of such coins could be a challenge.