Ok this is probably top secret but here is what the top minds suggest(Pinky and the Brain).
Place one watch with faceplate that is slightly radioactive (the name of the material escapes me at the moment lets call it iridium).
Remeber your sub history as they placed the radioactive material in the Proteus.
Now when the gray lady goes down and stays away to long we contact those friendly people with the satelites (Enemy of the State)
and have them swing there sensors across the body of water. They will detect the increased radiation from the watch and give you the GPS coordinates.
Again remember them tracking the Proteus with diminutive radar antena.
Then a EPA group will drain said body of water to discover the source of the increased radiation.Your sub will be found but will probably be encased in place
do to no storage area for atomic waste.
Mike can you do something about that witch avatar. It seems to have had to many pep pills.
Maybe a glasses of warm milk to slow her to a more pleasing motion. Thanks.