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If it was and English historical drama in the late 50's and 60's chances are it was in Black & White. For the following reasons.

1. Black and white made it easier and less obvious for any miniatures, or stock film. Just like Sink the Bismarck!.
2. It was probably cheaper at the time. The UK didn't have the budgets Hollywood had.
3. Subject matter. Black and white seems more fitting for a grim tale. Also gives it a more historical look to it.

well you said 50's but I think you mean '50s (the decade of the 1950s - see how the tick mark replaces the "19"?)
Both "50's" and "'50s" are correct forms of reference to the decade of the nineteen-fifties. There are regional variations (most UK reference sources prefer the non-apostrophe ending 50s), while both can be found widely used in the USA. The use of "50's" is an older usage but still quite acceptable.
See:
http://www.english-for-students.com/50s.html
https://public.wsu.edu/~brians/errors/50s.html
Different style guides may specify one usage or the other.

I don't think color films were the norm in the . well you said 50's but I think you mean '50s (the decade of the 1950s - see how the tick mark replaces the "19"?)

Color films actually weren't quite as common in the 50s as you seem to think. Even in the late 50s there were still a lot of films being shot in black+white. However most big budget films (which A Night to Remember is) were shot in color by this time, so it is a bit of an anomaly in that sense.

Could someone tell me what happened to the young married couple? I know they were fictitious, but there were indeed young married couples who died on the Titanic. As I recall, this couple was killed when the smokestack collapsed on them, is that correct?
Yes, they were killed when the smokestack fell on them. But it wasn't at all unusual for such an "unhappy" event to be in a 1950s film, or in films from earlier decades for that matter. Individual tragedies have always been incorporated in films to arouse audience sympathies. Quite common. And in a film like this it's the sort of thing you'd expect to see, to bring home the enormity of the tragedy.
In truth I've never had much sympathy for this couple. They adamantly refused to do anything to save themselves (not even to save the wife) until far too late. They were both so wrapped up in some foolish romantic haze about facing their fates together that it's difficult to muster much feeling for them. Only near the end did they try to save themselves. Presumably, when at the last moment they saw the stack about to fall on them the romance of dying together abruptly became less appealing.

Could someone tell me what happened to the young married couple? I know they were fictitious, but there were indeed young married couples who died on the Titanic. As I recall, this couple was killed when the smokestack collapsed on them, is that correct?
I found it interesting that this film would decide to have an unhappy ending for that couple, although audiences of that period liked happy endings.
I very much like the black and white; it made filming, I'm sure, much easier. It made the story a stark contrast: a fight for survival; you lived or you died, no in between; black and white.
An excellent film that I have been waiting a long time to see.

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Well I think it dates the movie correctly. Plus they had fewer technology for their special effects back then. The B+W would have probably allowed them to get away with more things. I find it hard to watch exterior shots of the ship because it just looks so fake lol. It's almost as if it's bricked to the ocean floor.

Actually, Three-Strip was available as early as 1935when it was used in the final scene of HOUSE OF ROTHSCHILD, and for the film BECKY SHARP. It was also used in the 1936 film RAMONA. By 1938-39, it was more common, but still extremely expensive, and with fewer cameras available.
There were some gorgeous films made in 1939, like DRUMS ALONG THE MOHAWK, DODGE CITY and WIZARD OF OZ, but I wonder how many more there would have been, if the majority of the TC cameras hadn't been hogged by SELZNICK and GWTW. (VBG)
I do hope he won't upset Henry

It does give it a more nightmarish feel for what the victims must have experienced that night.

It was to incorporate archival film. But it was also a stylistic choice to give it the feel of footage from 1912. And, if you watch it, it really does feel like a postcard from that era.

I find the black and white picture really effective for the horror of that night also.
The world is your lobster.

I think it works from an artistic standpoint as well. The clothes are very period for a 1950s movie (an era in which period clothes had a decidedly 50s bent to them). With the close attention paid to sets and costumes, it almost looks like a moving period photo.

The film's producer Bill MacQuitty claimed that the main reason ANTR was shot in black and white was the need to incorporate existing b/w film clips like the launching of the Queen Elizabeth and other stock footage, plus various scenes taken from an earlier German Titanic drama.

Thank you, that makes a lot of sense. While I'm a big fan of film of that era (50's and 60's), I'm not particularly knowledgeable about the technical aspects. In this film, the B&W "feels" right.

Color positive film was available almost from the dawn of movies but it is difficult to work with as exposure errors cannot be corrected.
Technicolor (3-strip) became available in 1939 and put to good useGone with the Wind, Wizard of Ozbut at great expense.
Kodak color negative film was invented in 1949. There were a couple intermediate systems that weren't altogether satisfactory, like Polacolor.
Even with the advent of color, 'dark' subject matter was often shot in BW. That would be my explanation.

It's twue! It's twue!