Fairfax and Montgomery counties are two huge, high-performing school systems that compete with one another for neighborhood bragging rights as well as national academic acclaim.

They set aside their rivalry Monday, however, when Fairfax School Board members asked their Montgomery counterparts to share hard-won advice on how to find a new schools chief.

Last year, Montgomery spent eight months looking for a replacement for retiring Superintendent Jerry Weast. In April, the county named Joshua P. Starr as its new schools chief.

Now Fairfax is embarking on its own search for a successor to Superintendent Jack D. Dale, who announced last fall that he plans to retire when his contract ends in June 2013.

Dale was hired in 2004 after a highly confidential process that left some community members feeling shut out. Fairfax board members have said they are eager to seek more public input this time around.

Montgomery’s message: Hire a search firm. Ask parents, teachers and other elected officials what kind of leader they want.

But above all, keep quiet — many attractive candidates, particularly sitting superintendents, can’t risk their names becoming public before they’ve accepted the job.

“You want as wide a pool of candidates, as deep a pool as you can possibly get,” said Montgomery board member Patricia O’Neill.

“They might be hesitant to come and interview if there’s any possibility that it’s going to be known back home that they’re out interviewing.”

O’Neill was one of three Montgomery school board members who spoke at a Fairfax board work session Monday. The others were current President Shirley Brandman and Vice President Chris Barclay.

Montgomery gathered a lot of public input early in their search, asking community members to describe the qualities they were seeking in the next schools chief.

The school system handed that “leadership profile” to Hazard, Young and Attea Associates, an Illinois-based head-hunting outfit that has conducted superintendent searches for some of the most prominent school systems — including for Fairfax in 2004.

From then on, the process was confidential. Résumés were guarded jealously. Interviews were conducted in discreetly, away from school system headquarters, so that no curious parent or prying reporter would catch wind of candidates’ names.

The three finalists did not address the public, but instead met confidentially with 16 community members — including parent advocates, employee union representatives and so on — who then offered feedback to the school board.

(The Maryland Open Meetings Compliance Board later said the Montgomery board erred when it created that community group in secret instead of in a public meeting. On Monday, O’Neill urged Fairfax board members to consult with their lawyers early and often.)

Fairfax school board members said they were thrilled for the guidance — and interested in further exploring Montgomery’s approach. But perhaps most of all, they’re ready to start searching.

“I want us to get started,” said Sandy Evans (Mason). “We’ve been given a gift of time” and should take advantage of it, she said.

Other tips:

Be on your best behavior. Superintendents don’t want to work for a dysfunctional board or a board that’s deeply divided during the hiring process.

“Many superintendents are not coming unless they have unanimity among the board. If you have a fractured board in that selection, it may totally nullify who’s going to accept the job,” O’Neill said.

Don’t limit yourself to candidates who already have experience running large school systems. “Your pool will shrink tremendously,” said Barclay, who said it was more important to look for evidence of the skills a person would need to lead a large system.

Montgomery chose Starr last year despite the fact that he was overseeing a relatively small school system at the time — Stamford, Conn., with 15,000 students and 20 schools.

Be aware: This process is stressful for teachers, principals and senior administration staff. “It’s something that you don’t necessarily think about, but it’s a huge part of this,” Barclay said. “Many folks have been hired under this superintendent so this is the only person they know, this is the only way they know, and it’s about to change — and everybody is feeling it.”