The compromise allows the groups to avoid paying for the coverage by certifying they are opting out, which then forces insurers to pick up the tab.
The groups have argued the certification process still essentially forces the groups to authorize the coverage for its employees, even if they are not technically paying for it.
A three-judge panel of the District of Columbia Circuit, including two new Obama appointees, pressed a Justice Department lawyer on those concerns.
The certification form still requires groups to "designate" a third-party administrator, U.S. Circuit Judge Nina Pillard said.
The issue is one that dozens of Catholic groups have raised in litigation, and many have received temporary injunctions, but no appeals court has yet ruled on the merits of the issue.
In the most high-profile challenge, the Supreme Court in January granted the Little Sisters of the Poor group of Roman Catholic nuns a reprieve from complying with the contraception requirement while its litigation continues.
The cases are separate from challenges brought over the same provision by for-profit entities, including arts and crafts retailer Hobby Lobby Stores Inc. The Supreme Court signaled in March that it might allow corporations to mount religious objections to covering employees' birth control as required under Obamacare.
Any ruling in that case could impact the outcome of the similar challenges from non-profit groups.
The Washington panel also pressed lawyers for the Catholic groups that brought the case, Priests for Life and the Roman Catholic Archbishop of Washington, on what would constitute a burden on religious groups.
"Is there anything a plaintiff could sincerely object to that wouldn't be a 'substantial burden?'" Pillard asked.
The Washington panel also questioned both sides in a second case challenging the Obamacare law, brought by Iowa artist Matthew Sissel. Sissel had seized on a Supreme Court ruling that identified the penalty the Obamacare law imposes on individuals who do not purchase health insurance as a tax.
Sissel argued the entire law then violates a provision in the Constitution that says legislation that raises revenue must originate in the House of Representative, and not in the Senate, as Obamacare did.
A lower court dismissed the case, but Sissel appealed to the circuit court. On Thursday, the panel homed in on what counts as a bill to raise revenue, questioning both sides on the issue.