The general types of things managers could measure would be their own activities, the employees’ perceptions of improvement in their managers’ communication behaviors and some operational outcomes that could be expected to improve because of the improved communication.
The ultimate measure of customer communication is sales. The trick is to find ways of tracking your communications against sales in a way that eliminates the effect of other factors.
Perceptions generally need to be quantified by a survey methodology administered to your key audiences. Behaviors are better measured by tracking outcomes.