Well for a written test, I think that it depends on what the applicants role as an Engineer will be. Are they going to be responsible for field work, or just sitting behind a desk doing design? Will they be making a thousand of the same machines, or one off custom equipment? New machines, or retro fitting new features into old equipment..... I think that you need to be more specific, before we can answer the question (this is a broad and demanding field). But you could ask troubleshooting questions if they are going to do field work, or design type questions like the coffee mug, to see how they think about a project. If they are fresh engineers, then this may not work though. The test I took when I was recruited from Bethlehem Steel; only about 2% would pass. And then they had an extensive 4 month training program afterwords to teach us the skills needed.
I would design questions, to show that the applicant can think beyond their training, and then don't forget, that they will need mentoring afterwords. The test can prove they are capable of learning what they need to.
-MUR