Collins said MAM trustees have raised about $70.5million in pledges to date, and about $33.5 million of that sum has already been paid.

The remainder will be raised in the months leading up to the museum’s scheduled opening next year — and beyond, Podhurst said.

With much of the museum’s share of construction costs already raised from private sources, Podhurst said, MAM officials are now focused on building the endowment.

“The key for the next year and a half is to get the endowment as high as we can get it,’’ he said, “so we can really do some great operational programming.’’

Museum trustees made a number of promises to ensure that the new building does not run into the same cost overruns and delays that plagued the Adrienne Arsht Center for the Performing Arts, which cost nearly $500 million to complete and experienced numerous delays before opening in 2006.

“After the performing arts center, I think that this community was really gun shy, as I can understand,’’ said Rose Ellen Meyerhoff Greene, vice president of the museum’s board of trustees.

But Greene said museum trustees — nearly all of whom pledged gifts to the campaign — have taken a personal interest in ensuring that the new building comes in on time and on budget.

“If you’re building your own home, you hire an architect; you hire a contractor; and then you watch every light socket put in the home,’’ she said. “That’s how we’ve treated this project.’’

Among the most important commitments made by MAM trustees was management of the building’s design and construction, which ensures that any cost overruns will be paid for by the museum and not the public.

“Those are written assurances,’’ said Michael Spring, Miami-Dade’s cultural affairs chief and one of the principal public officials overseeing the project.

Spring said museum trustees signed a contract promising to raise $120 million in private donations, though there is no timetable specified for raising the funds.

If MAM fails to meet those fundraising goals, then museum trustees and benefactors will be expected to make up the difference, Spring said.

Miami-Dade and the city of Miami, which contributed about $2.8 million in bond funds to the project plus the land for the building, exercise some oversight of the project. For instance, all project costs are paid first by MAM, then submitted for reimbursement to the county and city.

Public officials also receive updates on the project through monthly meetings with museum officials, and annual reports required for receipt of bond monies.

But much of the responsibility for the project’s success rests with museum trustees.

With their own skin at stake, Collins said, museum officials have hired teams of consultants to help manage construction costs, and to gauge future operational expenses.

“We have spreadsheets, and spreadsheets, and more spreadsheets,’’ Collins said. “We really feel confident we have a handle on it.’’

According to the museum’s projections, operating costs for the new building will more than double from the current $4 million a year to about $11 million annually.

Some of that additional operating cost may be borne by the county, which already contributes about $2 million a year to the institution. But county officials have not yet made a commitment to increase funding of the museum.