• Federal regulators on Sunday said they will cover customer deposits at Silicon Valley Bank and Signature Bank up to their full amount instead of the typical $250,000 limit.
• For small businesses, choosing a bank can be a weighty decision.
• Here are some tips for making sure you pick the right one.

For small businesses that have been keeping their money at Silicon Valley Bank — which collapsed last week — the good news is that they will be made whole. The same holds true for customers of Signature Bank, which was shut down by regulators Sunday.

Yet they now need to find another place to keep their money — and they and other small firms may fear a similar calamity elsewhere.

"They probably are thinking they need to use a bank where they'll have confidence that their deposits are safe, that they won't go through this again," said certified financial planner Douglas Boneparth, president of Bone Fide Wealth in New York.

"I know there are plenty of regional and smaller banks that are in fine financial health and would love to be the recipient of new relationships with small businesses," said Boneparth, who serves on CNBC's Financial Advisor Council. "But a lot of people's knee-jerk reaction will be to go to one of the big names in banking."

A 'bank run' on SVB was the catalyst

SVB's collapse occurred after it told investors Wednesday that it needed to raise $2.25 billion to shore up its finances. The news caused the bank's stock price to plunge, and panic-induced withdrawals quickly followed — a so-called bank run. Regulators shut down the bank on Friday and seized its deposits.

While accounts at banks are generally covered for up to $250,000 per depositor per ownership category by the Federal Deposit Insurance Corporation, a big concern at SVB was the money above that amount. The bank generally catered to venture capitalists and startups in the local area and elsewhere in the U.S., and as of December, about 95% of deposits at the bank were uninsured.

However, on Sunday, regulators approved a plan to ensure that clients of SVB — which just a week ago was the nation's 16th-largest bank — will get all their deposits back. The plan also applies to Signature Bank, whose customers also withdrew funds en masse.

For small-business banking clients, the plan should offer some reassurance.

For starters, the message is that when a bank fails, customer deposits will be covered for an unlimited amount, Boneparth said.

"How temporary or permanent that is, we'll find out," he said. "But for right now, that's welcome news."

FDIC coverage may be enough for some firms

Additionally, for some small businesses, the FDIC coverage at their bank should be sufficient.

"If you're a small business with never more than $250,000 in deposits, and your bank fails, it won't be an issue, other than a big inconvenience," Boneparth said.

Consider multiple banks, check financial stability

You also could consider having accounts at different banks, depending on the complexity of your business, said CFP Marguerita Cheng, CEO of Blue Ocean Global Wealth in Gaithersburg, Maryland.

"You can have a primary or main relationship for payroll," said Cheng, who also is on CNBC's Financial Advisor Council. "You can also have a relationship for Treasurys or cash reserves or a merchant account." Merchant accounts accept payments from customers via debit or credit cards.

It's also important to check the financial stability of banks you do business with, said CFP Cathy Curtis, founder of Curtis Financial Planning in Oakland, California, and also a member of the council.

"Look up the bank's financial statements, ratings and reviews," Curtis said.

She also recommends looking for banks that offer specialized services for small businesses — for example, a dedicated business banking team, merchant services or business loans or lines of credit.

Additionally, be sure you ask about fees, interest rates, monthly charges or balance requirements. It's also important to understand their online and mobile interface, Curtis said. "Is it sophisticated or clunky?" she said.

Additionally, you can ask other business owners who they bank with.

"Find out if they are happy with the customer service and business services provided," Curtis said.