Ok, being a very creative person, I had often made my own strategy games when I was younger. I made so many, it turns out, my friend mentions games I made that I can’t even recall! When I was in junior high, I had written up the rules for a submarine war game. The game was really complex in terms of realism (damage control, distress calls, flooding, etc) however I had a roadblock in it- neither player could see one another unless they detected them. I didn’t want to use an ‘honor system’ regarding movement (not because I was worried about cheating, but because of possible errors in the game) Basically the game would have been played on a hexboard. Later, reading the rules for ‘Battletech’ (a tabletop game my friend and I played) I discovered a thing called ‘double blind’. This was a set of rules used when neither player knew their opponent’s position, making a really gripping game of hide-and-seek. The problem was, this required a referee to track each player’s movements. I wanted to find a way to do this with two players. Recently, I found two solutions, but both have setbacks-
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Each player has a large circular disc which covers a large radius of hexes. The player’s submarine is in one of the hexes in the disc; when he moves he moves the entire disc. Using sonar and other detection, the disc can be shrunk to get a more accurate guess as to the opponent’s position, or even removed when the exact position is found. The problem with this is that each player still has a vague idea where his opponent is; a player couldn’t be ambushed or caught off guard because of the disc. Nobody would be the victim of a crazy ivan when they’d know they’d be charging into their opponent’s killzone.
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Each player indicates their positions and move normally. However, in order to get a firing position, they have to go through the normal avenues of sonar and listening to set up a firing solution. The problem here is obvious- each player knows where the other is, they just can’t shoot each other right off the bat.
I can admit that so far, I am stumped. Can anybody offer some advice (possibly anybody who plays naval wargames?)
Presents a neat logistics problem. 
Maybe the board could be something like a game of concentration. All the hexes are covered with anonymous face down cards. Some/two of the cards(or perhaps underneath the card) is each player ship counter(s). When a “detection turn” takes place all the cards in the appropriate range around the detecting ship are upturned.( I guess the other player would have to look away and only get to see if his ship is detected, sorry slight honour system)
If you want to give approximate location then require the player to place a token within x-hexes of his ship.(I guess that requires a little honour system too)
I’ll think more…
Assuming you trust your opponent to be honest it sounds like you’ve simply got a much more complex version of Battleship going on here. Basically, you state your intention to ‘scan’ a particular area of the map. To some extent I guess you’ll have to accept some ability for each player to vaguely guess whereabouts his opponent’s ship is as scanning ranges are likely to be limited…thus if you scan a particular area your opponent knows at least partially how far you can possibly be from a given space (this is also dependant on just how big the battle area is and whether you include underwater obstacles that might interfere with scanning). If the area scanned contains the opponent’s vessle then he or she must indicate that they have been found. Note that there would be a ‘public’ map that both players could see and personal maps that each player keeps their own notations. Presumably after the game is over the other player’s map could be inspected to see that course and headings were dutifully kept and not changed. Someone could still probably cheat if they really tried but it would be difficult. The best solution for this would be a laminated hex board that could be written on with a grease pencil.
It is here where you can use your disk idea. Whether the opponents ship is found depends on their speed, depth, range and so on. A quick calculation can determine just how precisely the opponents ship has been spotted. Subs rarely know right off the bat exactly where an opponent is but generally get a vague idea and then firm up their plot. Based on the precision that the opponents ship is pinpointed you can put varying sized disks on the main board that cover the area where the ship is in although it may be anywhere in that area. Over time (each turn) you can either grow that disk or shrink that disk based upon the players success at keeping and improving the contact (or not improving as the case may be). You could also add some sort of pointer that indicates bearing on the disk if that information is known as well.
Of course, the other player will still have a sense that they are getting pinpointed but I’m not sure how to avoid that without a computer (i.e. the computer keeps track and essentially acts as an impartial referee letting each player know what they are allowed to know and nothing else).
I think your solution is to use two identical hex boards out of each other’s sight, and trust the honesty of your opponent. Or learn computer programming, and play it on two computers over a modem.
I would look to Stratego for a good model. Basically your pieces all face you, and look identical to the opponent.
Some variations on this could work depending on your particulars; for example each piece could be like a checker, but with an icon on one side indicating what it is. You would lay them all out, icons face down, on the board, and move by swapping piece around.
Or you could use Battleship as a model, where essentially each player has a private grid, and they can interrogate each other about a specific sqaure or squares on it (not sure if this is the same as what Whack had in mind).