Ask HN: Presenting current employer projects to potential employer?

Let's say you have an upcoming interview with a potential new employer who's in an entirely different industry from your current one, and they'd like you to give a presentation on one project from your past that you've worked on from start to finish. I.E. what was the scope of the problem, how did you go about solving it, etc. To test technical ability, leadership, and presentation skills.

If your only projects that are big enough in scope to be a presentation like this are ones you're working on at your current employer (and you're not aware of any NDA you've signed), how do you deal with the situation? How do you know what is OK to present and what is not, if you don't want to tip off your current employer that you're looking (in other words, can't ask current employer if this is OK)? Is it reasonable to take a project you're working on now and change all the details about it, but keep the same gist of it?