When you’re managing managers, your job is twofold: You need to make sure they’re producing good work (as with any employee) and that they’re effectively supporting their teams.
People learn how to lead from their bosses, so set a good example. Manage your people in the way that you expect them to manage their own teams. In your one-on-one meetings, ask directly about how they are coaching people and giving feedback. This sends a signal that these things are important. But don’t dictate exactly how the managers should manage. You have to allow them to lead in their own way, and they need to figure out what’s authentic to them. It also helps if you can boost their profile with their direct reports. Praise them publicly, ask for their advice in front of others, or assign them part of a presentation that lets them show off their expertise. The people who work for your direct reports look to you for clues as to how they should feel about their managers. If you respect the person and the job she’s doing, so will they.