Karen Holling, a 47-year-old homemaker in the Phoenix area, was planning to drive to Los Angeles with her stepmother later this month for a three-night stay. The pair began to reconsider as cases of the Delta variant rose. They’re both fully vaccinated, but worried about the Covid-19 risk—and that businesses might shut down, keeping them from fully enjoying the trip. This week, they decided to call it off until case numbers improve.

“We just don’t want to risk it,” she says. They were able to get a full refund on their hotel, she says, because they canceled with enough advance notice.

With cases of the more-infectious Delta variant rising and summer travel even more chaotic than usual, some people are having second thoughts about their vacations. While plenty of people are forging ahead, others are considering modifying their plans—canceling, postponing or pursuing lower-risk activities without nixing the whole trip.

Here are some strategies if you’re reconsidering.

Visitors at the Eiffel Tower in Paris registered for Covid-19 tests this week.

Visitors at the Eiffel Tower in Paris registered for Covid-19 tests this week.

Photo: Daniel Cole/Associated Press

Check local Covid-19 case counts and changing restrictions

Just as many travelers check the weather forecast before their trips, they should also make a habit of checking the local Covid-19 case count, says Jessica Justman, an infectious-disease specialist and associate professor of medicine in epidemiology at Columbia Mailman School of Public Health. “Things change certainly from month to month, and even from week to week,” she says.

Cities, states and countries continue to update their travel guidance. The city of Chicago, for example, recently added Florida, Louisiana, Nevada and the U.S. Virgin Islands to its travel advisory list, encouraging unvaccinated individuals to obtain a negative Covid-19 test result no more than 72 hours before arrival in Chicago or quarantine for a 10-day period upon arrival.

If you have travel insurance, look closely at the fine print

Whether you can get a refund for Covid-19 concerns depends largely on what types of bookings you made, and whether you have specific types of travel insurance. Cancellation coverage is still somewhat limited in standard travel insurance plans, says Stan Sandberg, co-founder of TravelInsurance.com, a policy-comparison site.

Basic trip-cancellation coverage found in many comprehensive travel-insurance policies includes cancellation for unforeseen circumstances, such as natural disasters, or an unexpected injury, illness or death involving you or one of your traveling companions, which would require a physician’s letter.

But if, for example, you are worried that your travel destination will become a Delta variant hot spot, a cancellation wouldn’t be covered under most standard plans, Mr. Sandberg says. Additionally, most plans don’t provide refunds for pandemic-related shutdowns, he says.

Covid-19’s Delta variant is proliferating world-wide threatening unvaccinated populations and economic recovery. WSJ breaks down events in key countries to explain why Delta spreads faster than previously detected strains. Composite: Sharon Shi The Wall Street Journal Interactive Edition

There are some policies that can aid travelers who choose to cancel in advance because of Covid-19 concerns. Shelby Dziwulski, chief executive of Authenteco Travel, requires all of her clients to purchase “cancel for any reason” coverage. This is often sold as a supplemental policy and will allow you to receive reimbursement for your prepaid and nonrefundable trip costs.

The policies can range from 35% of the cost of your base insurance plan to 60% of the cost, says Mr. Sandberg. Under these policies, you could cancel a trip over concerns related to the Delta variant, but most policies only reimburse 50% to 75% of total trip costs, he says. Most policies also require you to cancel within 48 hours of your trip.

Know where it’s easiest—and hardest—to get refunds

If you don’t have travel insurance and are trying to modify reservations on your own, you might have an easier time getting refunds on certain parts of the trip. Hotels and rental cars may be the easiest to get refunds on, because you often aren’t paying the full amount in advance, says Teri Goins, president of Campbell Travel. Some hotels, however, will offer a discounted rate for prepayment and then specify that there can be no cancellations, or will only allow cancellations up to a certain date, she says.

Whether you can get a refund for a home stay will depend largely on the host’s policy. An Airbnb booked with flexible policies allows full refunds for cancellations made at least 24 hours before check-in. The company said guests can contact the host of the property to see about rescheduling.

Plane-ticket refunds depend on whether your fare was fully refundable. Most airlines waived change fees, so while you wouldn’t have to pay to reschedule your flight, you would have to pay for any difference in the cost of the fares.

Cruises, tours and events packages are typically the most difficult to get refunded, which is where supplemental insurance can be helpful, Ms. Goins says.

Consider ways to lower risk without canceling your trip

The Centers for Disease Control and Prevention has said those who are fully vaccinated don’t need to wear masks in most situations, with some exceptions, including when traveling by plane, bus or train. But some doctors say it’s a good idea to take additional precautions on vacation.

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Dr. Justman is urging more caution than she did a month or two ago because of rising case counts. “Wear your mask, avoid crowds, try to keep 6 feet of distance between you and others as much as you possibly can,” she says. And the more time spent outdoors, the better.

Max Folio, 26 years old, of Elk River, Minn., is planning to go to France at the end of the month to visit his partner. Although both of them are fully vaccinated, they are wary of rising Delta cases, and have decided to spend much of the trip outdoors to minimize the risk. “I don’t want to get sick, he doesn’t want to get sick, and we don’t want to get the people around us sick, so we’re going to play it smart,” he said.

Write to Allison Pohle at Allison.Pohle@wsj.com