When a man needs a necktie that looks great with tweed, he could do worse than to consider wool tartan and madder silk neckties like the versions from Drake's London in the photo. Perhaps not these precise patterns mind you, since I saw them first and have them on order, but something similar.
Tartans and tweed were both popularized in Scotland, so it's no wonder they go together. Of course, if a man is to wear a tartan properly, he should confine himself to patterns that are not reserved for a family or organization that he doesn't belong to. The Black Watch, Caledonian, Hunting Stewart, and Jacobite tartans, for example, are wearable by anyone who likes the pattern these days. They are usually executed in wool, but I've seen versions in cotton madras, Irish poplin and other materials so it's just a matter of looking around for the proper combination.
And if the tartan's a bit too Scottish for a man who may have been born elsewhere, there's always the madder necktie. Madder is the tweed jacket necktie of America's Eastern universities, to the extent that anyone at an American university still wears neckties. A special gum silk is processed into muted neckties with green, chocolate, medium blue, and yellow grounds and a chalk hand that's similar to fine suede. The stuff used to be called ancient madder, but after a couple of chemical process changes to make production more environmentally sound, the ancient part of the name was dropped. Fortunately, the makers didn't try to name it modern madder.
Madder and tartan. Real tweed wearers will have neckties from both.