As the future of Roe v. Wade hangs in the balance, several major U.S. companies including Apple, Citigroup and Yelp have taken public stances in support of abortion care and promised to cover employees' travel expenses to access the procedure. 

The Supreme Court is expected to make a decision on Dobbs v. Jackson Women's Health Organization, a Mississippi case that directly challenges the right to abortion established by Roe v. Wade nearly 50 years ago, sometime this month. 

Following the leak of a draft decision on the case in early May, which showed that the court is poised to overturn Roe v. Wade, more employers have introduced new health-care benefits or expanded existing policies to support employees in obtaining an abortion, regardless of what the court decides. 

Still, the logistics of such offerings remain unclear, including how companies will protect employees' privacy and if state legislatures could come after corporate insurance policies as part of an abortion ban. 

How will abortion benefits work?

In April, Yelp announced that it would cover costs for employees and their spouses who must travel out of state to access abortion care in response to the Texas law that bans the procedure after about six weeks of pregnancy.

Following the announcement, executives received an "outpouring" of messages from leaders at other companies asking them "how to do the same," Miriam Warren, Yelp's chief diversity officer, tells CNBC Make It. 

"They want to know how the benefit works, what employees' feedback has been, everything right down to the brass tacks," she says. "Many companies, like ours, are thinking about abortion care, and thinking really hard about it — not just how to safeguard employees' right to health care, but what it means as a brand to stand up for this right." 

Johnny C. Taylor Jr., the president and CEO of the Society for Human Resource Management, has also fielded calls from business leaders interested in offering benefits to cover abortion care. 

"One of the safest, least controversial moves a company can make without isolating employees or customers who don't support abortion is tweaking their benefits policy, whether it's offering a travel stipend or getting abortion to be categorized as an elective procedure," he explains, which would be covered under an employer-sponsored health-care plan.

Both Warren and Taylor predict that companies introducing abortion benefits would follow Apple, Citigroup, Tesla and other well-known companies in focusing on travel reimbursement for employees who have to leave their state to access the procedure. 

Companies are getting creative in how they offer this benefit, too, Taylor notes, to avoid potential legal and administrative hurdles, whether it's offering employees a one-time bonus or setting up donation-based relief funds that employees and their spouses can access if they need to travel for an abortion. 

In all cases, companies need to consider how they will protect the privacy of employees who do seek an abortion, Warren says. Under Yelp's policy, for example, employees submit travel receipts directly to their health insurance provider for reimbursement, so no one else at the company would know.  

Ultimately, Taylor adds, "the overwhelming majority of CEOs want to remove barriers to people who choose to have an abortion to access the procedure, without taking a position on whether abortion is good or bad."  

Will more companies take a public stance on abortion?

The thorniest issue companies have faced since the draft opinion became public — and during the heated debate over abortion access that's followed — is whether to make a public statement in support of or against the court's decision, if Roe v. Wade is overturned. 

"I'm convinced that organizations are going to do their best to avoid making any public statements, because it is such a divisive issue," Taylor says. "You might see some larger companies take a stance, but we forget that most companies in America are small and medium-sized … and we're not seeing any indication that those CEOs are willing to do this, and risk losing talent or customers."

Instead, Taylor predicts that companies will quietly tweak their benefits policies or send an internal memo to employees once the court's decision is announced. 

Warren, however, expects more employees to call on their companies to take a firm stance on abortion in the coming months. A new Gallup poll has found that 55% of Americans consider themselves "pro-choice."

"Folks might feel like they don't have to speak up about abortion care right now because we're in a bit of a holding pattern until the decision is announced," Warren adds. "But I can't imagine that they'll feel the same ability to stay quiet if Roe v. Wade is overturned."

Check out:

How the CEO of Planned Parenthood is preparing for a future without Roe v. Wade: 'We've been planning for this moment for years'

Corporate boards continue to make slow progress toward gender parity, new report shows

Janet Yellen: Overturning Roe v. Wade would be 'very damaging' to the economy, women

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