I interviewed somewhere a few months ago that asked me to reimplement something they'd built already, trying to be as pixel-accurate as possible. They paid me really well for my time (~$2k), they time-boxed it, they gave me a copy of their boilerplate framework, and they kept an open channel of communication with me so that I could ask questions. That, plus personal on-site interviews, felt like one of the best interview experiences I've ever had.

It took up a lot of my week, though, and I know it would be tricky to be interviewing at multiple places at the same time like that. Others have mentioned portfolios, which is an idea I think makes a whole lot of sense.