In Pennsylvania, the insurer Independence Blue Cross has "started an outreach program to welcome" new enrollees, said company spokeswoman Judimarie Thomas.
"In the first step we are calling new members and inviting them to ask questions about their health plans, and we are also asking a few basic health questions," Thomas said. "Over the next few months we will continue to contact new members through mail and email with information on our wellness programs, our online tools and resources, on how to use the medical benefits and prescription coverage, and other important programs or benefits."
"Where appropriate, we will refer new members to our medical management programs or encourage them to see their primary care doctor," Thomas said.
Another "Blue" taking a proactive approach is in Florida.
Jon Urbanek, a senior vice president at Florida Blue, said, "When people sign up with us, they're definitely going to get some electronic communication." In most cases they're getting a welcome call.
Those communications offer new enrollees free biometric screenings—measuring weight, blood pressure, cholesterol and other physical levels—which can be performed by a nurse at one of the the insurer's 17 retail locations.
"We don't put these things in the passive sense, we want them to be used," Urbanek said.
"The population that we're seeing on the [Obamacare] exchange, they are skewing older, they're skewing a bit more female, and from risk pool perspective, we anticipate right now that they are higher risk," Urbanek said. That makes it even more important to get those enrollees to undergo biometric screenings, so any health problems can be revealed and possibly addressed, he said.
"If we can get people more involved in their health care, that's one of the things that ultimately is going to have an impact on cost," he said.
Urbanek said the insurer is seeing 5 to 7 percent of enrollees accept the offer for free screenings—which tracks the rate seen by insurers nationwide who make similar offers.
But he noted that this is "significant and dramatic when you think about the dollars that are spent on health care."
In New York state, new insurance company Oscar has seen a much higher adoption rate with a program that pays new enrollees $10 to answer 10 questions related to their health, called "10 for 10." That health risk assessment questionnaire takes as little as five minutes to fill out.
(Read more: Fed watchdog probes 'flawed' Obamacare exchange )
Oscar's co-founder Kevin Nazemi said that about 67 percent of enrollees have taken up Oscar on the offer, and answered the questionnaire.
"This gives an early warning to us, and enables us to do proactive outreach," he said.
—By CNBC's Dan Mangan. Follow him on Twitter