A provision in the 2010 health care law requiring contraceptive coverage for women without copays has gotten most of the press.

But much more is at stake for women if the Supreme Court overturns the health care law. Starting in 2014, the law bars insurance practices such as charging women higher premiums than men, or denying coverage for pre-existing conditions that could include pregnancy, a Caesarean-section birth or a sexual or a domestic violence assault.

Even excluding maternity coverage, the National Women's Law Center found that nearly one-third of the most commonly sold insurance plans charged women aged 25 to 40 at least 30 percent more than men for the same coverage (PDF).

"Invariably, non-smoking women are charged more than men who smoke," said Judy Waxman, vice president for health and reproductive rights with the women’s law center.

While about 14 states have already barred insurers from charging women more, such restrictions will be universal in 2014 if the law stands.

On the flip side, women older than 55 are sometimes charged less than men the same age, Waxman said, a difference that will also even out in 2014.

Opponents of the law, including Grace-Marie Turner of the conservative Galen Institute, say the law’s restrictions on charging women more than men distort the insurance market in ways that can affect everyone. Raising costs for some men could result in fewer people overall purchasing coverage, driving up costs for everyone, including women, she says.

Other provisions, including providing contraceptives without a copayment, will also drive up costs, she says, and the rule also affects women business owners.

"Telling Catholic women business owners that they have to cover contraception and sterilization doesn’t give them more choice, it gives them fewer choices and it takes away their religious freedom," Turner says.

In addition, an expected 10 million more women are expected to gain coverage in 2014 as a result of expanded Medicaid coverage to people earning up to 133 percent of the federal poverty level, which is about $14,850, according to an estimate from the National Women's Law Center.

Women are also affected by provisions that require insurance policies sold through state-based exchanges to include maternity coverage, starting in 2014 and that mandate no copays for preventive services such as mammograms to screen for breast cancer.

Those provisions, along with pilot projects aimed at slowing health care costs by changing the way doctors and hospitals are paid, make the law "the most important advance for women’s health in decades," said Kirsten Sloan, vice president of the National Partnership for Women and Families.

She said the law "makes it easier for women and families to buy insurance, keep insurance and afford that insurance."

The court could reject all of the law, uphold it, or just toss parts. If it invalidates the requirement that nearly all Americans carry insurance, the key issue in the Supreme Court case, the Obama administration and opponents have asked the court to cancel related provisions that require insurers to offer coverage to all who apply and to not vary premiums based on gender or health.

If court throws out those provisions, "then we’re back to a situation where not everyone can get coverage, and insurers can charge whatever they want in the individual market, as they do now," Waxman said.