I know it is possible to obtain replacement medals for U.S. servicemen; see http://www.archives.gov/veterans/replace-medals.html for details.
On the other hand, I don't know what the process is for obtaining a medal if one was never issued in the first place. You say your grandfather received a commendation (rather than an accommodation as you say) for saving a shipmate from drowning. Whether that would translate to a specific medal, I can't say. The Navy and Marine Corps Medal might fit this situation, although in the case of a lifesaving action it requires that the action involve risk to one's own life. See https://awards.navy.mil/awards/webapp01.nsf/%28vwAwardsDisp%29/AW-10052085MLYF?OpenDocument. If you or your mother have the original commendation, that might help make your case. You might begin at the U.S. Navy Awards website (https://awards.navy.mil/) to see what you might be able to accomplish.
Any formal request from your family should be in the name of your mother since she is next of kin to your grandfather (next of kin = parent, spouse, sibling, child) rather than in your name. The next of kin has more standing than someone who is not next of kin in a case like this. You can do the legwork in the sense of drafting letters or preparing forms but it is your mother who should sign any formal request, if possible. If not, go ahead and make the request in your name and hope for the best.
Ron Carlson, Webmaster
Armed Guard / Merchant Marine website