An emotional response worthy of Shakespeare is pretty common when internal applicants are denied a promotion. “There’s a feeling that the psychological contract has been broken,” says Kathryn Dlugos, an assistant professor of human resource management at Pennsylvania State University. The spurned candidate is probably thinking something like, “If I’m not moving up with my current employer, why not? They owed me.”

Such feelings of betrayal may dissipate over time. But what happens next is bad news for employers: Rejected internal applicants often decide to quit. “The risk that they might leave is actually very high,” says Dlugos. “And the cost of replacing those people and needing to train and develop them can be very substantial.”

On average, companies receive 7 to 10 internal applications for every job they post. So what can they do to mitigate the risk that they’ll lose valuable employees who, for whatever reason, weren’t the lucky person chosen for the role?

In a recent paper published in the Academy of Management Journal, Dlugos and her co-author, JR Keller, an assistant professor of human resource studies at Cornell, offer several suggestions about how to navigate the sensitive matter of rejecting internal candidates....