When booking a weeklong yoga retreat, Amanda Levy signed up for a special package. Called “digital detox,” it promised a 15% discount if Ms. Levy, a sales executive at a San Francisco social-networking company, would agree to leave her digital devices behind, or surrender them at check-in.

“I am constantly on my iPhone and checking my email,” says the 29-year-old, who admits she sometimes “feels naked” without her smartphone. “But it was nice to be able to shut it off. It gave me an excuse to feel OK about not checking in.”

With hotels, resorts, and travel companies scrambling to fill rooms, a small but growing number are rolling out “unplugged” and “digital detox” packages to entice people who need a push to take a break from their screens.

Marketing the deals on Twitter, Facebook, and their own websites, many hotels are offering discounts. Others are focusing on amenities designed to reduce stress, including spa treatments, kayak lessons, and guided hikes.

Starting this month, guests at the Renaissance Pittsburgh Hotel can book “Zen and the Art of Detox” on some summer weekends. The Hotel Monaco Chicago offers anyone who reserves its “tranquility suite” the option to add a “Technology Break.” Others with similar packages include the Quincy in Washington, D.C., the Teton Mountain Lodge & Spa in Teton Village, Wyo., the Lake Placid Lodge in Lake Placid, N.Y., and Via Yoga, a Seattle company that specializes in luxury yoga and surfing retreats in Mexico and Costa Rica, including the one Ms. Levy took in April.

The services take similar approaches. Typically, they ask travelers to surrender their electronic devices upon check-in. In return, concierges provide them with old-fashioned diversions, from board games to literary classics. (Most, but not all, also yank TV sets and telephones from “detox” rooms.)

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