The Caldwells in Scotland are lowlanders and do not have an intrinsic affiliaton with any tartan. The family has intermarried with many other Scots families over the years and many of these families have tartans. Consequently you will find that the Caldwell's of different families will be affiliated with many tartans (and often on opposing sides). I was told when I was young that we could use the McPhail tartan but that was because we had relations the McPhails on my father's mother's side. Unfortunately apart from this my family has studiously intermarried with "tartanless" lowlanders. Consequently if any Caldwell's wish to associate themselves with a tartan then any one will be appropriate. I am sure that you will be welcomed into that clan.
Its good to see that tartans and whisky are accepted all round as being a mark of "Scottish-ness" as historically tartans were not welcomed in the lowlands and the lowlander drank beer. Highlanders thought of as Gaelic speaking barbarians. This is as opposed to the English-speaking, "sophisticated", and trouser wearing Lowlanders.
The "need" for tartans arose as a fashion thing in Victorian times and many of the principal houses of the lowlands adopted their own tartan in fairly recent memory.
By the time tartans became a fashion thing there were no Caldwell's left of sufficient aristocratic rank in Scotland to sponsor their own tartan and therefore we must be content with trousers.
At the time when we were possibly closer to the throne and may have had some claim to a tartan (if we had not been anti-highlander at the time) the chances are that the families we may have been closely associated with enough to "borrow" their tartan would be one of the lowland families of:
More, Wallace, Stewart, Cochrane, Sempill, Montgomerie, Cunninghame in roughly that order.
The ancient lowland Caldwell's would have had no truck with a tartan and the only Highlanders they might know were those that had emigrated to the lowlands for whatever reason (or rough cattle drovers turning thieves in hard times).
By all means "adopt" a tartan (it is good) but I don't think there ever was a "Caldwell Tartan" and we have never been a sept of a Highland Clan.
And what did the Caldwell's wear before trousers? Well this has been a source of mirth to the English since about the Roman times when we were known as "Picts".
Anyone for adopting the "Pict's Tartan"?