Jennifer Buettner was taking care of her young niece when the idea struck her. The child had a nagging case of hypochondria, and Ms. Buettner’s mother-in-law, a nurse, instructed her to give the girl a Motrin tablet.

“She told me it was the most benign thing I could give,” Ms. Buettner said. “I thought, why give her any drug? Why not give her a placebo?”

Studies have repeatedly shown that placebos can produce improvements for many problems like depression, pain and high blood pressure, and Ms. Buettner reasoned that she could harness the placebo effect to help her niece. She sent her husband to the drugstore to buy placebo pills. When he came back empty handed, she said, “It was one of those ‘aha!’ moments when everything just clicks.”

Ms. Buettner, 40, who lives in Severna Park, Md., with her husband, 7-month-old son and 22-month-old twins, envisioned a children’s placebo tablet that would empower parents to do something tangible for minor ills and reduce the unnecessary use of antibiotics and other medicines.