In general, you don't pay royalties to the authors or owners anymore; there are copyright clearinghouses for each industry that will take your money, give you a license, and see if they can find anybody to give the money to... The US Register of Copyrights refers to these as "orphan works", and they currently play an important role in shaping proposed modifications to copyright policies, not to mention the GoogleBooks lawsuit.
That rule about "95 years after death" does not exist in the USA. It is 70 years after author's death, and that only applies for unpublished works, or works created or published after 1977 (with copyright notice required until 1978). If the author was an employee or anonymous, then it is 95 years from publication or 120 years from creation, whichever is earliest.
It also depends on whether you mean "musical compositions" (sheet music) or sound recordings. For instance, there is no US federal copyright protection for ANY sound recordings published in the US prior to 1972. However, violators can still be sued under STATE laws (common law torts), possibly until 2067 when federal law is set to preempt state copyright laws on those recordings. I would suppose that every new violation restarts the statute of limitations.
If you're concerned about sheet music published between 1922 and 1978, you may need an expert to figure it out for you. There are multiple overlapping rules (publication, notice, registration, renewals) that had to be complied with at the right times. See the Cornell chart linked below for more details.