At the Colorado Center for Reproductive Medicine, a popular destination for women hoping to preserve their fertility by freezing their eggs, Dr. William Schoolcraft, the founder and medical director, has started to notice something different: more of the women are arriving with company.

“I see these patients come in, and they’re with two elderly people, and I’m like, ‘What the hey?’ ” Dr. Schoolcraft said.

The gray-haired entourages, it turns out, are the parents, tagging along to lend support — emotional and often financial — as their daughters turn to the fledgling field of egg freezing to improve their chances of having children later on, when they are ready to start a family.

The technology to freeze a woman’s delicate eggs to be used later, when the eggs being released by her ovaries may no longer be viable, has improved sharply over the past decade. There currently is no single source of data on the number of women who are choosing to freeze their eggs, but doctors in the United States say the practice is slowly growing.