Assuming that Jamie doesn't die after the last episode, it seems most likely that he will be taken captive by Dany's forces. While many posts have discussed the importance of having such an important prisoner over Cersei's head, I haven't heard anyone talk about Widow's Wail.

Jaime (I believe) is still carrying the sword as he falls into the water, and it will for sure be confiscated upon fishing him out. They made a point to say its name during Jaime's confrontation with Lady Olenna, for the first time since Season 4. Next episode, Jorah will probably arrive at Dragonstone or reunite with Dany somewhere in between Oldtown and Dragonstone. In the books, Dany makes a point to promise Jorah a Valyrian Steel sword when she becomes queen. While she doesn't make this promise in the show, it would be an effective gift in recognition of Jorah's persistence and loyalty even in the face of his certain death.

Another place the sword could end up is in Jon's hands, who has the most use for the sword in his upcoming battle(s) against the WW.

Anyone have any other predictions for the sword's potential ownership?