Copyright protection for older texts if the author cannot be found?

I would need more information to give a definitive answer, but the following may be helpful for the period you are dealing with: If the work was created and published WITHOUT a notice of copyright before 1964, then it has entered the public domain. If the work was published WITH a notice of copyright before 1964, it may be protected still if it was renewed for a second term. However, if it was NOT registered for a renewal copyright term, then it would be in the public domain. For the second renewal term to be currently in effect it would need to have been registered within the 28 year term of the first notice of copyright, which would extend the term for up to an additional 47 years. If this is a real concern, you can hire a lawyer or pay the copyright office to perform renewal searches. At any rate, I do not think any Fair Use analysis is particularly needed here, one exception might be if this is solely for educational purposes.

The work is still be protected by copyright (95 years from the date of publication).
The practical thing to do (I’m not a lawyer so this is the non-legal advice…) would be to ask a qualified librarian to help you conduct a thorough search if you haven't done so already. A good institutional librarian should be accustomed to advising researchers about fair use of copyright. They can also put you in touch with a publishers' copyright licensing body who could advise you on what to do in this case. Otherwise, to play it safe – possibly a drawback for your anthology – you should omit the work, or at the very least, keep a record of all attempts to find the author (search results, screenshots etc.) so you that you can prove that you tried to find the author should they catch up with you.