Super CONFI was developed from CONFI (q.v.) to search for grand slams by two balanced hands. (reference: Bridge World Magazine, February 1975).
The workings of Super CONFI are similar to CONFI. Opener makes an opening bid (or rebid) of NT that has a range of three or less points. Responder judges that a grand slam is close, so he checks for controls by making the first "meaningless" bid. For example, over 2NT (20-21, say) most people play:
3C Stayman 3D/H Transfers into hearts/spades 3NT to play 4D/H Transfers into hearts/spades
Thus, 3S can be used for CONFI (a small slam try) and 4C can be used as SUPER CONFI (a grand slam try).
After Super CONFI is initiated, opener rebids the number of controls she has. With a 20-21 balanced hand, she rebids 1st step minimum number of controls (5 or maybe 4) 2nd step 1 more than minimum (6) 3rd step 2 more than minimum (7) etc (although having 2 more is usually enough to justify promoting the hand to a higher range).
If there are enough controls for a grand slam (ie at most one control is missing), responder can rebid in any suit. NOTE that in CONFI the suit must be at least Qxxx, but in SUPER CONFI the suit can be any quality-- since your side can't be missing more than the K of it.
Opener and responder than bid their suits up-the-line and after agreement, they can bid the grand in the suit. NOTE that opener or responder can choose to bid 7NT even after a fit is found; however, grand slams are so rarely bid at matchpoint or IMPs that 7 of a suit should be sufficient. (7NT should be bid if there are solid side suit(s)).