For those who are eligible for a COVID-19 vaccine and desperate to get one, the region’s hospitals offer a glimmer of hope. They’re winding down vaccination of employees and other health-care workers, and some are now turning to older patients or those at high risk of serious complications from the coronavirus.

Their methods and eligibility rules differ, but they are united on one message: Don’t contact us. We’ll contact you.

“We love our patients. We want to help you, but please don’t call us,” said Jonathan Stallkamp, interim chief medical officer at Main Line Health.

Another theme is not to put all your eggs in their basket. If you can find a vaccine somewhere else, go for it. Demand from patients dwarfs the doses of vaccine that hospitals will be able to offer, although there is hope that supply will soon increase. “Take the first offer,” said Tony Reed, chief medical officer at Temple Health.

Another piece of advice: Sign up for your system’s health portal and respond quickly to messages. That’s how many health systems are first contacting eligible patients.

Area health systems said 55% to 65% of their employees have gotten vaccinated so far. Many are on second doses now. Others are still signing up for shots, but in small enough numbers that there’s room for high-risk patients now.

» READ MORE: Where can I get a COVID-19 vaccine in the Philly area? Use our lookup tool.

Temple initially focused on its own staff, but then expanded to include other health workers. It now has a well-functioning system, Reed said, and it makes sense for it to do more community vaccination. Plus, larger hospitals are the ones equipped with the ultracold freezers that can safely store Pfizer’s COVID-19 vaccine. “One of the things the city has wisely done is that those of us who have the skill set and the freezers are getting the Pfizer vaccine,” Reed said.

Einstein Healthcare Network, Penn Medicine and Temple have also applied to provide community vaccinations for the general public in Philadelphia. Main Line Health plans to use some of its vaccine allotment at community sites aimed at underserved populations in regions it serves.

Here’s what the hospitals that responded to our queries said about how, or whether, their patients can get vaccine from them:

Crozer Health

Crozer Health is offering vaccines at Crozer Chester Medical Center in Upland, and Delaware County Memorial Hospital in Drexel Hill to people who are eligible according to state guidelines. People who qualify can register through Crozer’s web-based system. The wait for appointments is now several weeks. Registrants will be contacted by email when openings occur. Hospitalized patients will not be vaccinated.

Crozer is also contacting organizations in the city of Chester to coordinate enrollment of qualified people who do not have access to computers or smart phones.

Einstein Healthcare Network

Einstein has hospitals in both Philadelphia and Montgomery Counties. Steve Sivak, head of Einstein’s vaccine task force, said his system never intended to vaccinate the general public, but now sees how eager patients are for shots. It plans to vaccinate within some of its hospitals through February, then, hopefully, shift to a community site in Philadelphia. He estimates that about 10,000 Einstein patients are eligible now in Philadelphia alone. Einstein now has about 3,000 doses on hand but doesn’t know how many it will get each week after those are depleted.

The system will vaccinate patients at its hospitals in Philadelphia and Elkins Park.

In Philadelphia, patients 75 and older, transplant patients or those with kidney disease, diabetes, and cancer are eligible. In Montgomery County, the list includes people who are 65 and up or have a wider array of risk factors.

To start, Einstein has asked primary care and transplant doctors and oncologists to identify patients they think are most at risk. Those patients are being called.

Jefferson Health

Jefferson, which has 14 hospitals in the region, is sending information about preregistration and appointment scheduling to patients through its portal. Eligible patients include those 75 and older, those with high-risk medical conditions, and patients who work in essential jobs that increase exposure.

A spokesperson said the system planned to start vaccinating patients in Philadelphia on Friday and will administer vaccines to patients from the system’s major locations in Philadelphia, Abington, and New Jersey next week.

“We anticipate that vaccine demand among our patient population will continue to exceed supply in the coming weeks,” Edmund Pribitkin, executive vice president at Jefferson Health and president of Jefferson Medical Group, said in a written statement.

» READ MORE: All your COVID-19 vaccine questions, answered

Main Line Health

Main Line Health started vaccinating patients last week at three sites: Lankenau Medical Center, Paoli Hospital, and its corporate center in Radnor. It will not be giving shots at all of its hospitals.

It is notifying eligible patients — people 75 and up — through its portal and is encouraging all patients to open accounts. Some doctors’ offices are helping people sign up.

Stallkamp said up to 20,000 patients are qualified for vaccines, and the system has slots for about 500 a day. “We’re not going to do this alone, and we can’t,” he said.

Penn Medicine

Penn referred a reporter to its website. It says Penn has started vaccinating Philadelphia patients who are 75 and up or have one of the four risk factors. Because vaccine supply is “very limited,” it is contacting patients who are at highest risk first. “As our supply of vaccine increases, we will continue to contact patients who meet the eligibility requirements to schedule their vaccine,” the website said. At the current rate, this phase is expected to take weeks.

Prime Healthcare

Prime, which operates Lower Bucks, Suburban Community and Roxborough Memorial Hospitals, does not yet have enough supply to vaccinate patients at Suburban Community and Roxborough Memorial. In Bucks County, the county registration site is routing some patients to the hospital for shots. Michelle Aliprantis, a health system spokesperson, said patients who qualify for phase 1A can get vaccinated at the hospital, but have to register with the county.

Lower Bucks and Suburban Community Hospital also hope to open vaccination clinics, possibly in mid-February.

» READ MORE: Yes, you still need to wear a mask after you get the COVID-19 vaccine. Here’s why.

Temple Health

Temple University Hospital is now vaccinating patients in Philadelphia. The system will later give shots at Fox Chase Cancer Center and at Jeanes Campus-Temple University Hospital. It is starting with about 6,000 doses, Reed said.

Temple is starting with patients currently receiving treatment for cancer and those who are at the top of an organ transplant list or who have recently been transplanted. After that, it will go to patients 75 and up and those with other risk factors. The system has asked primary care doctors and specialists to recommend patients with the highest need for vaccine. Patients will be notified through Temple’s portal or by email first, but will be called if they don’t respond.

Asked how long it will take to vaccinate patients in this phase, Reed said, “I’m going to be optimistic and say June.”

Tower Health

Tower Health will soon begin notifying patients who are 75 and up about its vaccination plans through its patient portal, said Mary Agnew, chief nursing officer. It may do some patient vaccinations as early as next week.

Tower will offer vaccine to eligible hospitalized patients while they are in the hospital. It is looking for community sites to vaccinate outpatients. Its first site will be an occupational health center in Muhlenberg. It is also in discussions with urgent care centers.

The system will have a call center in place by next week to contact patients who have difficulty using computers.

Cooper University Health Care

Things are different in New Jersey where most hospitals are not directly vaccinating their patients, according to Wendy Marano, a spokesperson for Cooper.

Cooper is, however, providing staffing to a community vaccination site run by Camden County. You can register at my.cooperhealth.org.

Virtua Health

The story is the same at Virtua, which is helping support Burlington County’s vaccination site at Moorestown Mall. That site is open to the general public, and Virtua patients receive no special priority. You can register at virtua.org/vaccine.

That site is now vaccinating about 1,000 people a day. If more vaccine were available, it could easily give 2,500 shots a day, said Rebecca Lynch, senior vice president and chief operating officer of Virtua Medical Group.

When more vaccine flows to the states, the system hopes to begin offering it to patients in its primary care offices.