When Pope Benedict XVI tendered his resignation Monday morning, he didn’t have to worry about finding a successor—the Vatican has a time-tested process for picking the next pope. But his announcement brought up emotional issues of mortality, identity, power that will be familiar to many chief executives who know that someone else will be sitting in their corner office one day. And when that CEO is running a family business, the process can get extremely complicated.

Tensions naturally underlie the succession planning process, as it forces CEOs “to face their own mortality,” says John Beeson, principal of the management consultancy Beeson Consulting, and author of The Unwritten Rules: The Six Skills You Need to Get Promoted to the Executive Level (Jossey-Bass, 2010). “They’re afraid that’s going to prompt their departure, before they’re ready.”

But add to the mix the logistical and emotional dynamics of a family-controlled business, and you’ve got a succession-planning task that can be challenging for any board of directors or general counsel to navigate. The overlap among family ties, family owners, and family employees or managers can make the situation even more complex.

“Having objectivity in terms of determining who is best qualified to take over the leadership role can be more complicated,” says Stephanie Brun De Pontet, a senior consultant with Family Business Consulting Group Inc.

The stakes for making the right leadership selection, though, are high. “A poor choice can fracture the board relationships—or in some cases can fracture family relationships,” says Beeson.

Not to mention the risks to the company’s brand or its growth potential, lest a bad decision about a CEO lead to reputational damage or in-fighting among family members.

“Having an objective, candid, open dialogue about this—that’s key,” says Beeson. “In the absence of that dialogue, some very unfortunate things can happen.”

A sound selection process can mitigate those risks by creating transparency and breeding confidence about who ends up taking the helm. “Having a well-understood, methodical process—that helps breed confidence in the ultimate choice,” says Beeson.

He recommends that boards ask not just who should be running the company in the future, but what skills the future leader should possess. “What kind of leadership will the company require based on industry trends and company strategy over the foreseeable future?” he asks.

Beeson also advises companies to implement a fair process for identifying and testing internal candidates—and to apply those measures to external candidates as well. “What job experiences would best develop and test these individuals?” he says.

With succession planning done far enough in advance, the company can also take steps to make sure board members get to know and trust possible successors, he says.

By being an advocate for best practices, “the general counsel can play a really important role here” Beeson says.

But general counsel of family businesses also need to be mindful in their approach. “You’ve got to be super careful, because if the CEO thinks you’re taking the side of another family [member or] group, you’ll probably be gone pretty quickly,” says Fredrikson & Byron attorney John Stout, who chairs the American Bar Association’s corporate governance committee. “These issues are so sensitive, you have to be very adept.”

Independent board members are in the best position to raise these questions, according to Stout: “A lot of times it’s the introduction of independent directors who really will be independent in their advice.”

Stout recommends involving outside board members that a family trusts “before these issues become inflammatory.”

Independent directors can come on either as “full directors,” says Stout, or as non-voting advisory members. In the latter case, such directors can’t cast deciding votes, but by sitting in the boardroom, they can contribute to discussions, and even propose and second motions.

Brun De Pontet agrees. “A lot of times founders struggle with letting go because their identity is so tied up in the business.”

But independent board members or in-house counsel can push CEOs for clarity on their plans for retirement, and how they envision their role in the company during retirement. “They can hold them accountable,” she says.

Creating a family council—which is made up of family members, but is separate from the company—can also be beneficial. A council can channel the views and expectations of a sprawling family, and provide a vehicle for them to give input on topics such as strategy and family values, the latter of which can sometimes “trump certain business considerations,” says Stout.

A family council can also come in handy for grooming successor directors, because younger family members can learn about the business. “Director succession planning is important, too,” Stout adds.