Is it or isn't it X

Can you approximate what you're looking for by putting partial info on the back of the card?

Another thought, though this might depart from what you have in mind: Does the 'matching' card have to be a SPECIFIC card? Or can it change game-to-game?

Suppose you have this setup:

1. Put cards into sleeves numbered 1-whatever such that you cannot tell which card is in the sleeve. This can be done with opaque sleeves and a pen, or by putting a numbered card into a sleeve and then the other card behind that.

If you don't like sleeves, you could just place the unknown cards face down, and then numbered cards or tiles face down on top of them.

You now have a set of cards which are identifiable by number but not by what they actually are.

2. Make the other set of cards (the ones that match the above set) indicate which NUMBER it matches - meaning for this game, this card matches whatever card is in sleeve #1.

So, you have a card from that second set, and to see if you've found it's mate, you look at the number only of one of the cards from the first set. If yes, you get to look at the card associated with that number. If not, then you don't.

That does what you're asking for, except it can't keep cards connected to SPECIFIC cards (the same cards they were connected to last game). If that works for you, then this should work.

I'll take a shot at this. I propose two solutions:

1.) Use folding boards.

You know how your Risk and Clue boards fold up so that they fit in the box? Use tiny, folding boards for "tiles." You can flip one side of the tile over (the correct side is clearly marked on the back with an icon, or with the words "flip me") to see what KIND of tile it is. If it's the "right" kind, you can turn the whole folding tile over. If it's NOT the right kind, you can just leave it folded over (or flip it back down, if there's a "memory" aspect to the game).

2.) Use plastic cups and dice.

You've got dice that come in - let's say - three different colors. Some of your game dice are weighted so that they'll ALWAYS roll a 6, and some are not. At the start of the game, you put one of each color die into the little plastic cups. You dump the dice in and flip the cup over before you can see how they land (you can put a small lip on the cups to make this easier).

When you reveal a cup, you know you're looking for rolls of "6" on a die of a certain color. If you see one, you know you've overturned the right KIND of cup, but you don't know if the die shows a 6 because that's how it landed or because it's weighted. If you don't see any 6's, you know you've overturned the WRONG kind of cup.

I feel like you are all misinterpreting the question (but I might be instead / as well).

I think the proposed problem is this: say you have tiles in the colors red, blue, green and yellow. Say you are looking for red, and you flip a tile. Normally, we would see the color of the tile (either red, blue, green or yellow) and, if it's red, take the tile, and if it isn't, don't take it. However, what we want instead is that we only see if it's red, or if it is NOT red; whether it is blue, green or yellow should remain hidden.

If the opponent is allowed to view the tile, then yeah, that's not that hard: just let the opponent look at it and say if it's red or not. But I suppose that's not a viable option either.

Otherwise, I don't see how this can be done, realistically, without electronics or some other kind of heavy contraption.

Hmm... Maybe you could use colored diagrams and images similar to the color blind tests? Where, to the normal eye, it just looks like a bunch of colored squigly lines and dots, but if you put a red filter over it, a number or a letter appears. Or even better, use cards with evenly spaced letters on them, where words only appear if you put the right black card with holes over it.

Something a bit like this.
http://heroeswiki.com/images/6/66/Hiros_message.jpg

I had something similar to this in a dungeon crawl solitaire I was designing a while ago (but then left unfinished, as usual).

In my game you would have, say, a locked door in one tile, and a key on a card. You would want to know if it was the right key for that particular lock or not. My solution was bar codes on the edge. You would not need a bar code reader or anything, just to place the key/card bar code in front of the bar code on the door on the tile. If they formed a pattern of continuous black and white lines, they match, meaning the key was the right one for that door; if not, the result would have some broken lines, half black, half white.

As long as the bar code is big enough to allow for some 200 lines (a regular bar code has 96 potential lines), the thing would be hard enough to "read" from a distance, but easy enough to see if it the halves matched. And it would not require any special printing, filter or device.

That has a lot in common with a line of hidden information mechanics that doho123 (Scott Slomiany) has been exploring for a while. You might be interested, in particular, in Dark Water Salvage (http://www.backglass.org/scotts/games/Shipwrecks/html/index.htm). It makes a great use of cards with holes to check only for specific information on other cards without revealing anything else. I had totally forgotten about it until I read your post.