I don't want to look it up, someone here I am sure is willing to do the leg work.

They can appoint someone to carry out the remainder of the term, I think, if the spouse seems best qualified (after all, they knew the Senator best) I suppose they would appoint her/him.

Most states have the rule that has the Governor appoint a replacement of the same political party as the deceased. Often, the spouse is very qualified to be appointed, and as has been said, would nornmally be closest to the deceased's thoughts and policies.

I do not know very many couples with the same thoughts and policies regarding politics.

But thank you both for your answers.