I've never worked with designers but we always let contractors know, either by phone or email (depends on how they've communicated with me) that they didn't get the job. If they ask why they lost the bid, I tell them.
I think what you're considering depends on how much time they spent on your project and whether they actually drew up plans. Usually there is a fee charged if they have to do anything beyond basic estimates.

Not getting the job goes with the territory, happens to every one. Thank him and say goodbye.

I wish all customers were like annz, I sure would appreciate at least knowing something.