The wealthy are willing to invest in maintaining their health, he said. More than half expressed an interest in getting full-body scans and genetic screening in order to assess their health, according to U.S. Trust's 2015 "Insights on Wealth and Worth." The survey questioned 640 individuals with more than $3 million in investible assets.
The trend toward testing was especially pronounced among high net worth millennials, who were the most likely to explore testing and have a doctor on retainer through concierge medicine.
Read MoreWorried about outliving your money?
However, scans and screenings can only go so far. When it comes to long-term care health care in retirement, 32 percent of those surveyed expect to stay in their homes with private home care, while 1 in 5 expect to be cared for by a loved one in their homes.
Long-term care can come with a hefty price tag, which is why U.S. Trust urges wealthy clients to consider elder care planning assistance with third-party providers who assist with issues like home care services and nursing home selection.
"It's a bigger financial impact and a bigger toll simply because the costs of health care and long-term care continue to escalate," Heilmann said.
Independent wealth advisor Debra Brede said many of her clients expect their wealth will allow them to effectively self-insure their long-term care health costs. But even for a couple with assets of $2 million, the toll of long-term care can derail financial plans, she said.
"The drag is on the remaining spouse, the one that's not sick," said Brede, president of DK Brede Investment Management outside Boston. "When the other one passes on and uses up a lot of the funds, the one that hasn't gone through it is the one that's going to suffer later."
"Don't look at long-term care or health issues as just financial," concurred Heilmann. "Look at them in terms of your family and the social dynamics that would result from that."