Imagine this workplace scenario: As the pandemic recedes, employees in Company X are given the option of returning to the office or working remotely. Mary decides to return to the home office in New York. Her former office mate, John, decides to remain in Omaha, Neb., where he has been living since the pandemic began.

They have the same titles and the same responsibilities. Should they also have the same pay?

That is just one of many compensation issues companies are likely to wrestle with in coming months, as businesses reimagine how to pay and reward employees in a world where some workers may not return to the office.

“The remote workforce is here to stay,” says Susan Schroeder, a partner at Compensation Advisory Partners, a national compensation consulting firm with offices in New York, Houston, Chicago and Los Angeles. “With that comes a shift in compensation structures.”

Adds John Boudreau, a professor emeritus of management and organizations at the University of California’s Marshall School of Business: “We have to admit that we don’t know [what the best policies are] and that there is going to be immense opportunity and variation.”

Here is a look at some of the compensation strategies and issues that companies may need to re-evaluate in the new era of remote work:

• Location-based pay. Before the pandemic, many employees received additional compensation if their principal office was located in an area with a high cost of living, such as New York City or San Francisco. That concept may become less straightforward in the remote-work era. Indeed, while some tech firms have said they won’t cut the pay of employees who relocate to cheaper areas and work remotely, others have indicated location will continue to play a role in compensation packages.

On the surface, that might seem fair: A dollar in New York doesn’t go as far as it does in Omaha, so the employee in New York is effectively getting paid less for the same job.

But many experts say that’s misleading because an employee’s ultimate worth is really about the quality of the work, not the geographic area where it is done.

“If you’re asking [employees] to do the same job that they did before, why do they become less valuable if they’re doing it from somewhere else?” ask Peter Cappelli, a professor of management at the University of Pennsylvania’s Wharton School, who says cutting pay for employees who relocate isn’t a good idea.

While remote work can give companies access to a much wider pool of talent nationally, Dr. Cappelli predicts that any employer that opts to reduce pay in these situations stands to lose its best employees.

Ms. Schroeder also sees danger in tying pay to where someone lives. “Once you pay different salaries for the same job based on where people live, you are on a slippery slope of pay fairness, equity and gender discrimination,” she says. It could expose the company to liability unless reasons for the pay differentials are properly disclosed and communicated, she says, adding that the best performing companies strive for a culture of pay transparency and pay-for-performance, where the results of an employee’s work matter more than location, she says.

• A two-tiered system. Even if the office worker and remote worker are in the same city, compensation and promotion issues will arise. When employees work remotely, they lose the career advantages that come from working and socializing face-to-face with their bosses, says Wharton’s Dr. Cappelli. “You can’t schmooze as well and find out [about] opportunities, so you pay a price by not being there,” he says.

That divide could also leave bosses unwittingly paying better salaries to those who work in the office versus those who work at home, says Dr. Boudreau. This is particularly true with new employees, since bosses typically are less familiar with them.

“The challenge is to make bosses aware of this,” he says, so they can take steps to level the playing field.

Having bosses set aside time each day specifically to engage with remote employees is one way to keep things more equal, says Erica Pimentel, an assistant professor at the Smith School of Business at Queen’s University in Kingston, Ontario.

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Human-resources departments may have to more closely review and calibrate pay decisions to ensure that compensation processes are being implemented in the same way for employees who work remotely as for those who work in the office, Ms. Schroeder says.

There also are risks that remote work will exacerbate gender-equity divides—say, if more women choose remote work due to family responsibilities, says Ms. Schroeder. This is something companies will need to closely monitor and consider when analyzing compensation packages, she says.

• More personalized perks. Perks such as company gyms, cafeterias and on-site child care won’t be of much use to remote workers, so companies may need to create offerings that are more open-ended or even personalized.

For instance, companies might consider giving a lump sum to remote workers to purchase items that protect their health and safety, such as ergonomic chairs and stand-up desks, says Dr. Cappelli.

And instead of offering commuter benefits, employers could subsidize parking for remote workers who live in urban neighborhoods, where they often have to pay to park, Dr. Pimentel says.

Ms. Schroeder says her company instituted a monthly “wellness perk” for employees of up to $250 a month in 2019. Whether they work from home or the office, workers can seek reimbursement for things that benefit their physical and emotional well-being, ranging from gym memberships to financial-planning advice to the payments they make on a Peloton bike. Many of the consulting firm’s employees also received an allocation last year to purchase printers and other office supplies, she says.

Child-care options and assistance paying for the care of elderly parents who live with them are the types of perks that are likely to be very popular with remote workers, says Dr. Boudreau. Bosses may be more supportive of such benefits, as well as scheduling flexibility, now that they have seen the reality of their workers’ strained home lives via Zoom meetings, he says.

Similarly, mental-health benefits also are being taken more seriously, Ms. Schroeder says. The issue is even being discussed by boards, which typically aren’t involved in crafting company benefit plans, she says. Employers are improving communication about these types of benefits and encouraging employees to use them, she adds.

• Project-based bonuses. Before the pandemic, many companies were moving away from project-based bonuses tied to individual and department goals, and instead basing bonuses on broader company targets such as revenue growth and profitability, says Ms. Schroeder.

That started to change with the increase in remote work, she says. To encourage teamwork, companies again began to incentivize “project metrics” that compensate individuals for accomplishing specific project goals.

Dr. Pimentel refers to this as the “entrepreneurialization” of work and says it could change employee relationships with their employers.

Under this scenario, employees become something more like “entrepreneurial consultants,” who are always working on projects for their company, she says. “Instead of filling 40 hours a week, you have this set of tasks to do, and if you finish them, maybe you get a bonus.”

The quality of work is what really matters, and it is what should be rewarded—no matter where the work is done, says Dr. Pimentel.

Mr. Horovitz is a writer in Falls Church, Va. He can be reached at reports@wsj.com.