Recent research from the Employee Benefit Research Institute finds that couples enrolled in Medicare could need as much as $413,000 in savings to cover their senior healthcare costs in full. Ouch.

But don't panic just yet. While that's clearly a large amount of money, there are steps you can take to save big on Medicare costs. Here are four you should incorporate into your strategy.

A person holding a tablet.

Image source: Getty Images.

1. Sign up on time

You get a seven-month window to sign up for Medicare initially. It begins three months before the month in which you turn 65 and ends three months after that month.

If you don't sign up for Medicare during that initial window, you can enroll later on -- but it might cost you. Specifically, you'll face a 10% surcharge on your Part B premiums for each 12-month period you're eligible for Medicare but don't enroll. And those surcharges, unfortunately, stick around for life. Avoiding them is a simple matter of signing up in a timely fashion.

That said, if you're working and are covered by a qualifying group health plan at the time of your initial Medicare sign-up window, you'll get your own special enrollment window once your employment or group health coverage ends. So don't stress if you don't need Medicare at or around age 65 due to being covered already.

However, make sure your group health plan is a qualifying one. That generally means a plan that has 20 employees or more.

2. Take advantage of the free services you're entitled to

As a Medicare enrollee, you're entitled to a host of free services. These run the gamut from yearly wellness visits to no-cost screenings for different conditions. There are also a host of vaccines that Medicare covers for free.

If you're new to Medicare, take the time to read up on the no-cost services you're entitled to. Getting ahead of certain medical issues could not only be a good thing for your health, but also save you money down the line.

3. Review your plan choices carefully during annual open enrollment each year

Each year, Medicare enrollees get an opportunity to make changes to their coverage during fall open enrollment, which runs from Oct. 15 through Dec. 7. It's important to compare your plan choices each year, even if you're pretty happy with the coverage you have already. You never know if there's a less expensive Part D or Medicare Advantage plan that will result in lower out-of-pocket costs.

Open enrollment is also a good opportunity to decide whether it pays to move from original Medicare (Parts A and B plus a Part D drug plan) to Medicare Advantage, or vice versa. It especially makes sense to compare your plan options if any of your medical needs have changed, such as if you've been diagnosed with something new or are on different medication.

4. Sign up for Medigap when you're eligible

If you decide to enroll in Medicare Advantage, you won't be eligible for supplemental insurance with Medigap. But if you stick with original Medicare, then it pays to sign up for Medigap coverage during your initial enrollment period. That window starts the first month you have Medicare Part B and are 65 or older.

What's the benefit of Medigap? In a nutshell, it could pick up the tab for the very expensive costs you might incur as a Medicare enrollee.

For example, this year, if you need a hospital stay, you'll pay $1,632 for your Medicare Part A inpatient deductible. And that only covers your first 60 days in the hospital. Days 61 through 90 will cost you a whopping $408 per day. A Medigap plan could cover that bill, easing your burden.

But don't wait to sign up for Medigap. Enrolling during that initial window will generally result in lower prices for coverage and more plan choices since you can't be denied coverage for pre-existing conditions during that time.

Medicare has the potential to be very expensive. But if you make these moves, you may find that you can spend a lot less in the course of taking care of your health during retirement.