Eager for Stamps in Your Passport? Head to Nebraska.

The Shelmadine Print Shop, which operates in a converted opera house, is one of 70 stops on a state tourism program that has stoked a pandemic-fueled competitive fervor among Nebraskans.

Travelers come by car, truck and RV, armed with “Nebraska Passport” books they get stamped at stops scattered across the state’s 77,000 square miles—ranging from “One of the World’s Largest Covered Porch Swings” to a church made from baled straw.

“It’s basically a tourism scavenger hunt,” said Becci Thomas, director of the Knight Museum and Sandhills Center in Alliance, a city of about 8,200.

There seems to be no shortage of oddball attractions for officials to highlight, especially in the far-flung towns outside Omaha and Lincoln where relatively few visitors go.

Nebraska’s Passport program, now in its 12th year, has included Carhenge, just outside Alliance, which is a sculpture made from old cars and trucks welded together in the shape of England’s Stonehenge.

The Bigfoot Crossroads of America Museum, in Hastings, Neb., has also been featured. “The place was kind of creepy, I wouldn’t have wanted to walk through it at night,” said Sandy Bice, a 69-year-old retiree from Cozad, Neb., who visited with her husband last year. (Harriett McFeely, owner of the museum, said it isn’t scary to most people. “A typical reaction is they are amazed,” she said.)

Ms. Bice and her husband, Tim, attained one of the highest honors in Nebraska tourism: Passport Champion, the past two years running.

Besides getting Passport Champion T-shirts, people who get all 70 stamps win prizes including a Visit Nebraska calendar, a canvas bag and the chance to be in drawings for one combo meal a week for a year at the Runza fast-food chain.

The Bices say they aren’t in it for the glory.

“There are just little gems and that is the truth,” Ms. Bice said. “People from New York City wouldn’t believe what it’s like in Nebraska. To me, I feel sorry for them.”

With Americans clamoring to get out after pandemic shutdowns, tourism officials expect banner business at roadside attractions. Already, in Arizona, Bowlin’s Travel Center’s “The Thing”—a supposedly mummified creature surrounded by exhibits of aliens and dinosaurs—is seeing more attendance, the manager says.

“People are getting sick of sitting around, just sitting,” said Mike Bingen, manager of the nearly 60-year-old tourist attraction in Dragoon, Ariz., whose billboards stretch for hundreds of miles.

The goal of Nebraska’s program is largely to showcase some of the state’s unusual and little-known destinations to its residents. Other states have tried similar programs but few are as large or long-running as Nebraska’s.

Nebraska Passport participation actually grew during the pandemic to a record 1,185 champions in 2020 from 914 the previous year, as locals stayed close to home, said Madison Johnson, coordinator of the program. She expects 1,400 champions this year and her office has printed 53,000 passport booklets to hand out, 3,000 more than last year.

New stops this year include the nearly century-old Meridian Bridge that provides foot access across the Missouri River to South Dakota. “I think a lot of people have no idea that exists,” Ms. Johnson said.

In all, 304 Nebraska businesses applied to be considered passport stops this year. The 70 winners are picked on the basis of variety and uniqueness and can’t have participated in the previous three or four years, said Ms. Johnson.

“The only rule is they have to be open at least one weekend day,” she said.

In Paxton, Neb.—where a downtown steakhouse with more than 200 big game trophies served as a stop last year—Leah Fote, owner of nearby Anne Marie’s Antiques and Gifts in an old railroad depot, decided to throw her hat in the ring.

“I decided there was nothing to lose, but no one likes rejection,” said Ms. Fote, 36. When she got an email a few weeks ago announcing “Congratulations,” she added: “I was super excited—then started my to-do list.” On a recent day, that included repainting walls of a shop filled with knickknacks and preparing a “selfie wall” for visitors.

With just days to go before the season opening, another passport stop— the Chuckaboo Station in Potter, Neb.—was still a construction zone. The front sidewalk was being replaced and a beer tap room was being built in the garage of the former 1930s gasoline station. Teran and Drew Enevoldsen now showcase her line of handmade candles there—including one that gives off the scent of an ice-cream sundae.

“I took two weeks of my vacation time to get ready for this,” said Mr. Enevoldsen, a local banker.

Ms. Johnson and other tourism officials held a Zoom call with the passport location operators last month, to let them know what they were in for.

Among other things, they were told to expect as much as a 25% increase in visitors. At Laughing Lamb Fibers, Mark and Tiann Goll said they weren’t too worried about the crowds. “We’ve had an entire second-grade class here,” Mr. Goll said in the shop in Sidney, Neb., that features 56 brands of imported wool, including from camels and alpacas.

Finding stops isn’t always easy. Dennis Drumheller said he and his wife Cindy ended up at the wrong end of a trail destination near Grand Island, Neb., where stamps were being given out at a nearby store. “You’ve got to be cautious at nighttime,” said Mr. Drumheller, a retiree from Gering, Neb.

Susan Morton won her first passport championship last year on the final weekend of the competition, ending her monthslong journey to get all 70 stamps at a coffee shop in Arnold, Neb. “I knew it was going to be tight, but I knew I had to do it,” said Ms. Morton, 62, an accountant from North Platte, Neb. “I treated myself to a movie theater in Broken Bow.”

Ms. Morton is ready to go after her second Passport Champion T-shirt this year. She started out May 1, the opening day of the competition, with a visit to Buffalo Bill Ranch State Historical Park outside her hometown. “They told me I was the first one of the new year,” she said.

Write to Jim Carlton at [email protected]