CHEYENNE, Wyo. — Matt Mead, the governor of Wyoming, , fiercely opposes ’s regulations, which could shutter hundreds of coal plants and deeply wound his state, one of 27 that are suing to block the plan.

Nevertheless, Mr. Mead, a Republican, has ordered his top environmental officials to prepare to comply with the president’s effort, known as the Clean Power Plan — to prepare for a future in which Mr. Obama’s climate change rules prevail and the country’s coal market is nearly frozen. Wyoming is one of at least 20 states that are moving forward with efforts to comply with the rules or to analyze alternative plans. Several of these states are also suing to stop the rules, according to experts who track state climate change policy.

“Obviously we’re suing and going to fight,” Mr. Mead, a former United States attorney for Wyoming, said in an interview in his office here. “But from my court experience, I know you have to prepare not to win.”

Mr. Obama’s is in legal limbo. the to halt the plan until after the states’ lawsuit is resolved. The case will go before a federal court in September, but it is widely expected to be appealed to the Supreme Court and may not be decided until 2018.

Republicans in Congress and their party’s presidential nominee, Donald J. Trump, have vowed to scrap the climate change rules. Senator Mitch McConnell of Kentucky, the majority leader, has urged governors to refuse to comply, and Republican governors in some states, including Indiana, New Jersey and Wisconsin, have issued “pencils down” orders to state regulators to stop work on the Clean Power Plan.

But in other states, governors, including some Republicans, and many environmental officials say that because the plan is so sweeping and ambitious, it would be imprudent to ignore it. The climate plan would force states to fundamentally transform their electricity systems, shutting down hundreds of power plants that run on fossil fuels and building new ones powered by the wind, the sun and other low-carbon sources, along with creating a need for hundreds of miles of new transmission lines.

Governors like Mr. Mead and state-level environment officials are making a political calculation: and appoints a new Supreme Court justice, Mr. Obama’s climate plan will probably survive.

In some cases, the governors moving forward with drafting state-level climate change plans are Democrats in places that have some form of climate policy in place, like and .

But in some Republican-led states, even those with “pencils down” orders, regulators are sketching out how they might eventually comply.

, and he’s not likely to look favorably on someone who’s crossways,” Michael McKenna, a Republican energy lobbyist, said of the wariness of politicians in the party.

“But if you’re a state environmental official and you think there’s a chance that Hillary Clinton is going to be president, you’d be unwise not to think about this,” he continued. “I feel bad for these state environmental guys. The ‘pencils down’ order puts them in a lousy spot, where some of what they’re doing has to be surreptitious.”

In South Carolina, after the Supreme Court halted the Clean Power Plan, C. Dukes Scott, the top regulator for Gov. Nikki R. Haley, a Republican, issued an order to stop all work on the plan — or even talk about it.

“I’m trying not to expend any resources on the Clean Power Plan, and I’m expending resources just talking to you,” Mr. Scott said in an interview.

But South Carolina regulators are moving forward with meetings on a new state energy plan — which, Mr. Scott conceded, will probably include discussion of how to reduce emissions from electric power plants. It will just not be called the Clean Power Plan.

“We’re still working on clean air, just not pursuant to the Clean Power Plan,” Mr. Scott said. He added that if the Clean Power Plan was upheld by the courts, South Carolina’s work on an energy plan that includes lower emissions from power plants could be repurposed in its work to comply with the climate plan.

Gov. Chris Christie of New Jersey, a finalist in Mr. Trump’s vice-presidential search, issued an executive stop-work order on the plan, and environmental regulators in the state said they had frozen all work on the climate change rules.

“New Jersey is strongly opposed to the Clean Power Plan, and we are not developing any compliance plan, nor do we intend to,” said J. Gregory Reinert, a spokesman for the New Jersey Board of Public Utilities.

But officials at PJM Interconnection, which manages electric power lines that run among 13 states, including New Jersey, said that a board made up of officials in all its member states, including New Jersey, had asked PJM to perform analyses of how they might comply with the climate plan, because it could create major changes in how electricity is produced and moved across state lines.

“If the rules move forward, that could change the entire way the electric transmission system works,” said Ray Dotter, a spokesman for PJM. “States want to be informed about this. If they’re not, it could cost them a fortune.”

In Virginia, supporters of Mr. Obama’s climate change agenda are trying to advance it with the “by another name” approach. Gov. Terry McAuliffe, a Democrat, backs the president’s climate change agenda, but in May, the Republican-majority Legislature passed a bill blocking the use of public funding for work related to complying with or even analyzing the Clean Power Plan.

So Mr. McAuliffe issued an executive order directing his secretary of natural resources to convene a working group that would put together a plan to cut carbon dioxide emissions in the state, using existing laws or regulations.

“I decided I wasn’t going to wait around for the court,” Mr. McAuliffe said. “I figured I had a way to get creative and do it my own way.”

“We will move forward with our own Virginia plan,” he added. “It won’t be called the Clean Power Plan, but the goals are similar.”

Because environmental officials in many states are preparing their climate change plans behind closed doors, ascertaining the exact number of states that are moving forward is difficult.

Environmental officials from 14 states, most of which are not taking part in the lawsuit, have sent a letter to the E.P.A. requesting technical help as they prepare for the plan. An analysis by Energy and Environment News, an industry publication, , including Republican strongholds like Arizona and Idaho, are moving forward with plans, and that an additional eight states are assessing climate plans but are not yet taking steps to carry them out.

“Other than for political reasons, it doesn’t make sense for states to stand down on their preparations,” said William Becker, the executive director of the National Association of Clean Air Agencies. “Very few states are just putting down their pencils and waiting.”

Mr. Becker said his association had held informational meetings and conference calls about the plan, including a recent call in which he estimated that officials from 50 state and local governments participated. He declined to identify the officials who had taken part.

“It’s difficult for me to out someone on this,” Mr. Becker said. “I don’t want someone to think they participated in a meeting and now they’re being ratted out.”