How do you obtain copies of US Navy ocean crossing certificates that belonged to a relative?
Ocean crossing certificates are not official Navy issue; most commands either make up their own (just a sheet with an emblem and info that may or may not get entered into your service record), or order printed and embossed ones from special commercial companies (Tiffany Publishing is a favorite). Those are ordered and received well after a ship gets home from the deployment, or at least they used to. These days they can probably transmit the order online. Nice, formal certificates are generally signed by the ship's CO.
Point is, you can't really get a copy per se; if you know the information for the ceremony/cert, you could order a replacement, but of course it wouldn't be signed.