This article is part of our special report on global shopping.

Sukeena Rao didn’t flinch when she picked up the phone.

One of her clients was panicking. She had arrived at a luxury resort in Indonesia for a friend’s 40th birthday party, and realized how poorly she’d packed.

Ms. Rao, 45, a two-decade, personal-shopping veteran at stores like Harrods and Harvey Nichols, didn’t flinch. She swung into action, securing a few key items at luxury stores in Singapore and dispatching them to the client via three flights, and had them hand delivered by a contact.

“When someone’s lifestyle is global,” Ms. Rao explained, “they don’t see any difficulties in procuring products for wherever they are in the world.”

This kind of support defines Luminaire, which Ms. Rao started this spring. Her partners are Harriet Quick, a longtime friend and former staffer at British Vogue, and Olivia Scanlon, a financier.

The 10-person company aims to find and supply must-have, even sold-out, items and deliver them anywhere. Luminaire’s declared niche is the global jet set and is differentiated by its round-the-clock responsiveness, according to Ms. Quick, 55.

“We offer a 24/7 service,” she said. “There will always be someone at the end of the WhatsApp message able to respond to you pretty quickly. The 1 percent is not located in one place — they’re moving between different continents and properties in their portfolio, and that helped shape the business.”

Those requests mostly focus on luxury brands like Prada, Bottega Veneta and Celine. Often, client requests will involve seemingly sold out or impossible-to-find limited editions. Ms. Quick and Ms. Rao’s careers have afforded them access to such seemingly sold-out stock. (The pair stresses that they always try to minimize the carbon footprint of such global shopping and shipping by securing the item from nearby, if possible)

Requests can also be more impromptu. Some clients simply relied on Luminaire’s taste and speed to fix their fashion emergencies. The firm might also receive an image of something spotted on the red carpet with a request from the client to wrangle the same piece. The team must then identify and source the piece. Luminaire refuses to work with clients who want multiples of a given item, in various colors or finishes.

“That’s not ‘new luxury’, which is about buying thoughtfully and carefully,” said Ms. Rao, though she says the likelihood that a client might try to resell excess items is also a factor.

Luminaire uses a private, club-style membership: Around 50 people pay its annual dues of £5,000, or about $5,900. They can then lean on the Luminaire team as much as they wish in return. “You could use our service daily if you wanted,” Ms. Rao joked. “And I’m not going to lie, we have a couple of clients who do just that.”

The company earns a 10 percent commission on new items, while a vintage search might be charged at a flat fee of £150. There are perks bundled with membership, too: Members might be offered the chance to book appointments with an in-demand hairdresser like George Northwood, or a personal consultation with the dermatologist and cosmetics entrepreneur Dr. Barbara Sturm. In December 2022, the company is opening a temporary townhouse in London’s Notting Hill for three days, and organizing intimate events — like breakfast for example — with Sabrina Elba, the wife of Idris Elba and a client, or the designer Brunello Cucinelli.

Luminaire isn’t alone: It’s just one of several start-ups that combine concierge-style service with a personal shopper’s skill. But while Luminaire focuses on high-end, globe-trotting shoppers, London-based SourceWhere, caters to a broader market.

It’s the creation of Erica Wright, 31, a former fashion publicist, who hit on the idea after her search for a pair of snakeskin loafers from Celine. In March 2014, she spent two months calling stores in Europe and hunting online before someone responded to one of her online posts. Try the Celine store in Indonesia, they said, as they’re still in stock. Ms. Wright bought them there over the phone, and had them shipped to the brand’s location in Singapore, where she would soon arrive on vacation.

She realized the business potential in providing that same service for other women like her — and established SourceWhere in January.

“If you’ve ever gone into a shop and seen something is sold out,” she said, “or you saw an item a few years ago and can’t stop thinking about it, you can turn to us.

“Place a request in our app for something present or past season, and our network of professional sourcing experts — they’re handpicked by me — will start the hunt.”

SourceWhere employs about 30 independent contractors around the world, which aims to buy and ship the item to the client — new or used depending on preference.

Brands like the Row, Balenciaga and Hermès are popular, and shoes are the service’s core category, Ms. Wright said, whether hard-to-find Chypre sandals from Hermès or sold-out Adidas Sambas. There’s no deposit or membership fee. It’s down to the sourcing experts to determine whether they charge a flat fee of £120 for an item, or opt instead for a commission of 10 to 15 percent.

SourceWhere retains an average 10 percent of that fee.

SourceWhere is no available in the United States, though Ms. Wright hopes to start there by next spring. And while Luminaire’s services are available worldwide, its founders say they have plans for an office in New York early next year.

Shoppers in the United States can also opt to work with someone like Gab Waller.

Ms. Waller, 28, is also acting as a consultant to SourceWhere as it plans to open in the United States. Ms. Waller, a Los Angeles-based Australian, has made a reputation over the last four years as a successful source via Instagram, where this informal industry first emerged.

She estimates that she has 1,800 active clients, including celebrities like Rosie Huntington-Whiteley and Hayley Bieber. Ms. Waller said that 90 percent of the requests she received for items come by direct message on Instagram. Her team of 20 also comprises independent contractors based around the world from Dubai to Singapore. Ms. Waller also recently added a new part-time staff member in South Korea.

Her services cost a flat $200 fee per item. When her contractors — or sourcing assistants as she calls them — obtain an item, they send it directly to the client in Gab Waller-branded packaging.

Footwear is a focus for her business, too, especially from brands like Chanel and Prada.

“The Chanel quilted sandals? We still get daily requests for those,” she said. Ms. Waller stresses that her service democratizes access to hard-to-find luxury goods.

“Clients tell me they feel intimidated going into those boutiques and uncomfortable because of how they were treated one-time, and we take that feeling away,” she said. For any shopper, though, the premise of her service is identical to that of SourceWhere and Luminaire.

“Is anything ever really sold out now?” Ms. Waller said. “No. It has to be out there somewhere.”