Yes, do ask them to design something if that helps you, but make sure you're having him/her design something on the fly that's related to your product, not a real problem you're actually having currently. When interviewing for my summer position at Milk, a part of the application process was re-designing a product that was similar to what Oink could eventually be. The exercise is supposed to be theoretical anyway, so this just furthers the amount of time a designer has to think about the problems and to just get to the solution. This could also be a take-home assignment where they allocate Xhrs to the problem.

More than anything, recognize that the purpose of this exercise isn't to see the designer's abilities (you should be able to see this in their portfolio of previous work), but more about how they approach problems and how they think critically. Understand that no one can ever really outline their design process specifically, but should be able to speak to about the way they solved problems in the past (again, see portfolio) and how they came to solutions.

Talk to them about what they view as "good design" and why they think it. A good designer is ultimately a good communicator and should be able to talk you through why they think it's "good" (in their opinion).

Something that might provide insight is this Behance interview of Ben Barry, Facebook's communication designer: http://the99percent.com/articles/7118/Facebooks-Ben-Barry-On.... It's not completely specific, but it will give you insight into the way most designers (in Silicon Valley, at least) think about their jobs and their work.

Hope that helps!