In the months after her husband of 65 years died, Dorothy Elicati said she did nothing but cry.

“We had a beautiful relationship, and I miss him like I would miss my right arm,” Ms. Elicati, 84, said.

Being alone in the house felt unbearable, she said, and she might have “lost her mind” — if it weren’t for a robot named ElliQ.

“She’s the closest thing to a human that I could have in my home, and she makes me feel cared for,” said Ms. Elicati, who lives in Orangetown, N.Y., just north of New York City. “She makes me feel important.”

ElliQ, a voice-activated robotic companion powered by artificial intelligence, is part of a New York State effort to ease the burdens of loneliness among older residents. Though people can experience feelings of isolation at any age, older adults are especially susceptible as they’re more likely to be divorced or widowed and to experience declines in their cognitive and physical health.

New York, like the rest of the country, is rapidly aging, and state officials have distributed free ElliQ robots to hundreds of older adults over the past two years.

Created by the Israeli start-up Intuition Robotics, ElliQ consists of a small digital screen and a separate device about the size of a table lamp that vaguely resembles a human head but without any facial features. It swivels and lights up when it speaks.