I'd echo everything @dieselgate said, and add this:
1. One key way to encourage honest feedback is for managers to be absolutely adamant that there will be no retaliation / retribution for giving honest feedback in good faith - even if it's critical of the manager, upper executives, or even the whole dang company.
2. Honesty is a two way street. If a manager wants honest feedback from his/her direct reports, they must have a history of being honest with those reports in turn.
3. On a related note, the manager should, I believe, show some vulnerability and openness to criticism by - when necessary - calling attention to their own mistakes and goof-ups. Saying "I screwed up, I'm sorry, but I'll fix $WHATEVER. I'm constantly working on getting better just like everybody else." goes a long way IMO.
4. For a manager, saying "thank you" and "I'm sorry" is a very valuable thing. If the only time you interact with your reports is to criticize them or to give them orders, they are going to become defensive and you are not going to get honest feedback. At least not until their exit interview. And even then it's a "maybe".
5. Show some genuine concern for the people who report to you. In 1:1's ask questions like "What can I do to help you achieve your goals" and so forth. And make it honest, don't just go through the motions. If you can't bring yourself to have some real empathy / regard / concern for your people, get out of management.