When she first joined Deloitte Consulting, she also moved from her native South Africa to the U.S. “A young partner in New York sat me down and said, ‘Bridget, you have tremendous potential, but you’re way too nice and polite.’ That was great mentoring!” she says. “It helped me understand the cultural differences. I quickly adapted.” She eventually became managing partner of Deloitte’s financial services business.

Then, in 2004, Van Kralingen joined IBM (IBM), which has included mentoring as part of its management training since Thomas Watson, Sr. founded the company in 1916. CEO Ginni Rometty, who tops our list, has mentored dozens of women and men, both formally and informally, and credits mentors for several key promotions in her own career.

At Big Blue, Van Kralingen recalls, “I had a sponsor who recommended me to run the financial services part of IBM’s business consulting services in Europe and Africa — in spite of my lack of IBM experience. His advocacy both helped IBM to take a risk on me and helped me navigate the job.”

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Mentoring, in other words, prepares people to move up, while sponsorship makes it happen. Both are “critically important,” says Van Kralingen, to anyone aspiring to get ahead. The not-so-great news: Most big companies now have embraced mentoring and, in the high-potential pipeline that leads to senior management, more women than men have had multiple mentors. Yet the percentage of senior executives who are female has barely budged since 1998, creeping up from 11.2% then to 15.7% now, according to nonprofit research group Catalyst.

A big reason why that’s so, according to one Catalyst study of 4,000 MBAs of both sexes, is that men are still more likely than women to have powerful sponsors. “High-potential women are overmentored and undersponsored, relative to their male peers,” observes Christine Silva, a Catalyst senior director. “Without sponsorship, women not only are less likely than men to be appointed to top roles, but may also be more reluctant to go for them.”

Because it requires a senior executive to spend his or her own political capital, and put his or her own credibility on the line, to give an underling a leg up, sponsoring someone is far riskier than mentoring them. “A sponsor is someone influential who will pound the table for you,” notes Claire Farley, who appeared on our 1998 list as head of North American oil and gas exploration at Texaco (since merged with Chevron (CVX)) — a job she took on while still in her 30s, thanks partly to a high-ranking sponsor. She’s now a managing director at private-equity powerhouse KKR (KKR) in Houston.

Farley adds: “There is so much that is impossible to know ahead of time about anyone’s leadership potential, it’s probably just human nature for people to sponsor people who remind them of their younger selves. So men tend to sponsor other men.”

For women who want to beat those odds, here are five ways to find a sponsor:

1. Build on a mentoring relationship. “Sponsorships often arise from deep and strong mentoring connections,” says Bridget Van Kralingen. “One thing I’ve found is that if you give feedback to higher-ups and share ideas, so that there are reciprocal benefits to the relationship, it’s more likely to lead to that person sponsoring you.”

2. Identify higher-ups who inspire you. “You don’t really choose a sponsor. They have to choose you,” says Claire Farley. “But you can improve your chances by first asking yourself who it is in the organization whose track record impresses you, and whose leadership style you’d like to emulate. Then try to stand out and get to know that person. Make your achievements, and your goals, known to him or her — without being too ‘political’ about it, because people see through that very quickly.”

3. Whenever possible, let a potential sponsor see you in action. It helps, Van Kralingen says, to keep an eye out for opportunities to work closely with a senior executive you’d like to impress. “You’re more likely to attract that person as a sponsor if he or she is very directly familiar with your work and has seen your performance firsthand,” she says. Accompanying sales teams when they call on clients, she adds, has led her to recommend several female stars for promotion — including one just last week.

4. Suggest improvements in the way things get done. “Many organizations are looking for critical thinkers who have the potential to be change agents. It’s how plenty of senior executives got where they are,” observes Claire Farley. “So ask a lot of questions, and learn the art of challenging the status quo in a way that doesn’t make people defensive.” It just might get you noticed by a sponsor who got his or her big break the same way.

5. Ask. The most direct approach sometimes works, says Van Kralingen, if there’s an assignment or promotion that you know a particular higher-up could help you get, but “don’t ask too many times. And before you ask, think strategically about it, and choose someone who might be able to help you move in any of several directions, depending on how circumstances change and different opportunities arise.” The broader your sponsor’s sphere of influence, the more likely it is that he or she can guide you into a niche where you’ll shine, so you can continue to move up.

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If seeking out sponsorship feels like asking a mighty big favor, keep in mind the findings of a Catalyst study that examined the impact on the sponsors’ own careers: Developing and promoting talent usually leads to bigger promotions and raises for the executives who do it.

Between 2008 and 2010, the research shows, managers who sponsored protégés earned an average of $25,075 more than their peers who didn’t. “A reputation for being able to spot talent and help nurture it is an asset to senior managers,” notes Christine Silva at Catalyst. “A culture of sponsorship is good for everybody.”