When one talks about confidence, a quiet knowing, what exactly does that mean?
I can only deduce that this confidence comes with fore-knowledge of a particular course of action leading to a predictable outcome.
In chess, this translates to knowledge - in fact, GMs have about 100,000 bits of this knowledge in the form of principles of the 3 phases of the game, plus other patterns of chess tactics such as mating patterns, even endgame patterns where 1 look at the arrangement of pawns can determine the course of action to take. It is this knowledge that players need to seek, whether through the study of games, or by deduction in the course of analysing his/her own game.
There will always be some positions where it will be impossible to calculate owing to the many ramifications of the variations pending on the player's understanding of the game. In fact, some of the correct moves may not even be discovered during the course of the game as that possibility may not have existed owing to the player's ignorance of the pattern / know-how. Hence, a strong player ought to have good erudition of what's been uncovered by past masters and how they are applied in today's competitive context.
Though computers can be a big help in terms of charting the variations from the opening to the middlegame, I don't think they can be of much help in the endgame as we all know, they do not reason the same way as humans do here. Countless examples have been found where the computer can actually derive nonsensical plans based purely on calculation whereas the human has better bearings based on heuristics derived from past experience.
Ultimately, the study of chess will be rewarded if one focuses on the relevant bits pertaining to his/her playing level and reinforces it in attempting to apply them in competitive games.