Source: http://www.vcbridge.org/ Presented by Mike Savage
The other day I held something like: 
A,
K10x, 
6543, 
AQJ63
partner opened the bidding 1 and the next hand bid 4 What should I bid? 5 will never get us to a slam if one exists as I have too many controls for partner to bid a slam. 6 would be an overbid as there might well be two losers in the hand. I’d sure like to invite a club slam while not committing to it. There needs to be a way to do that—and after some thought, there seems to be a good method to do it.
4NT over 4, specially over a 1 (or even a 1) opener by partner, should not be used as any kind of Blackwood (ace or control asking). Some might play 4NT here as a natural bid, but the frequency of occurrence of that type of hand seems too low to be worth it. Others might want 4NT over 4 to be used as a take-out for the two unbid suits. Lastly, you might use 4NT as a slam try in opener’s minor.
Rather than pick just one of these possible meanings for 4NT over 4, here is a way to combine two of them. Playing this method you can bid 4NT as a try for slam in partner’s minor suit or to show a two-suiter in the unbid suits, asking partner to pick between them. Here is how it would work:
| 1-4 – 4NT |
Club slam try or a red two-suiter | ||
| (diamonds and hearts, the unbid suits). | |||
| 5 |
Shows a minimum with no interest in club slam. | ||
| Pass | Has a club slam try but | ||
| is giving up. | |||
| 5 |
Has a red two-suiter and is asking | ||
| partner to chose between them | |||
| 5/5 |
Accepts club slam and is bidding | ||
| his longest red suit or, if equal, the stronger. | |||
| 5NT | Wants to play in 6 or six of a red suit (pick-a-slam). |
||
| 6 |
To play. | ||
| 6 |
Pass o correct to 6 |
||
| 1-4 – 4NT |
Diamond slam try or a rounded | ||
| two-suiter (clubs and hearts, the unbid suits). | |||
| 5 |
Shows longer clubs than hearts (or the stronger if of equal length). | ||
| Opener might or might not accept | |||
| a diamond slam try if responder has one. | |||
| Pass | Has a rounded two-suiter. | ||
| 5 |
Shows a diamond slam try | ||
| 5 |
Shows no interest in a diamond slam | ||
| and opener has longer hearts than clubs. | |||
| Pass | Has a diamond slam try but is giving up. | ||
| 5 |
To play with a club/heart two-suiter | ||
| 5NT | Wants to play either 6 or six of a rounded suit (pick-a-slam). |
||
| 6 |
Pass or correct to 6. |
||
| 6 |
To play | ||
Over a 4 preempt, you could use 4NT to simply be a slam try in opener’s minor (my choice).
1-4 4NT = A slam try in clubs.
5 = To play with no interest in a club slam.
5, 5 and 5 = A cue-bid of opener’s lowest 1st round control.
1-4 5 = To play with just enough values and clubs to prefer to play 5 than to defend 4.
1-4 4NT = A slam try in diamonds.
5 = To play with no interest in a diamond slam.
5, 5 and 5 = A cue-bid of your lowest 1st round control
1-4 5 = To play with just enough values and diamonds to prefer to play 5 than to defend 4
Instead of using 4NT over 4 as a straightforward slam try in opener’s minor, there are couple of other possible usages of 4NT that come to mind. Responder could use 4NT to show that you have longer length in the unbid minor than you have in opener’s suit. This is classically done with 6-4 in the minors but easily might be 6-5 or 7-5. This usage might get you to the best minor game—or even slam.
Another possible usage is to use 4NT over 4 to show either a slam try in opener’s minor or a slam try in the unbid minor. With no slam interest, opener will rebid 5 and responder will pass or correct.