Save vs nuke or die

There are certain skill checks whose outcome is unknown until the inevitable happens. Disarming a nuke before opening the case that would set it off. Disabling the ICBM's warhead before it launches. If these things don't get done right it will be too late later on.

So, how do you handle this with your players? More important than that how do you handle dice in these situations?

Let me present a few scenarios:

1. Rolls is done in the open against a target value GM previously mentioned.
2. Rolls are opposing. Player rolls and GM rolls. The player can see the player's roll but no the GMs. The GM keeps the roll secret until the player decides.
3. Rolls is done in the open against a GM set value, but it is hidden from the player (inside a cup). The roll is revealed after the player decides to open the case or not.
4. Rolls are opposing. Player rolls and GM rolls. The player's roll is done in the open, but the GM's roll is hidden and can't be touched by the GM until the player decides.

These examples go from total disclosure to the player (roll 1) and given the player the option to decide based on that outcome to having no clue as to what happened (roll 3). Rolls 2 and 4 can give a hint of how well the character did, but the player can't be sure the roll succeeded until the GM reveals the roll. Roll 4 leaves no room for fudging as the GM can't modify the roll.

What's your thought on each? How would you handle each situation? Do you prefer a open roll over the hidden? Do you want to at least know a little of your outcome? How to decide otherwise right?