[William Cloud Hicklin]

Note also that the Stone of Emyn Beraid remained in the Elves' keeping, in fact they made pilgrimages to look in it: which I think implies strongly that was the only one available to them.

I suppose it's worth wondering whether The Noldor brought any of the Stones into Exile with them.

Arguing for this view is the fact that they wound up in Eressea, not Valinor. However, it might be considered that Finarfin had gone all Vanya in the interim and was no longer interested in hi-tech gadgets, so just handed them over. Indeed it appears the Eresseans had no more use for them by the late Second Age, perhaps due to developed powers of Osanwe or something.

Arguing against this view is the fact that they are never mentioned in the First Age legends: indeed at the Nirnaeth Fingon and Maedhros had to communicate by beacon; nor did anyone have contact with Turgon (whom one might assume to have had one). However, it is likely the case that Tolkien never got around to backwriting the Palantiri into the pre-existing legends.