Exhibit 99.1

FOR IMMEDIATE RELEASE

Contact: John E. Ahern President and Chief Executive Officer NMT Medical, Inc. (617) 737-0930 jea@nmtmedical.com

NMT Medical Announces Settlement

of Patent Infringement Lawsuit Against AGA Medical

Agreement includes $30 million payment to NMT that will be shared with inventor

BOSTON, March 28, 2006 — NMT Medical, Inc. (Nasdaq: NMTI), an advanced medical technology company that designs, develops, manufactures and markets proprietary implant technologies that allow interventional cardiologists to treat cardiac sources of migraine headaches, stroke and other potential brain attacks, announced today that the Company, along with Lloyd A. Marks, MD (“Dr. Marks”), has settled its outstanding patent litigation with AGA Medical Corporation (“AGA”).

In the suit originally filed in March 1999, NMT claimed that AGA manufactured and distributed a septal occlusion device that violated U.S. patent No. 5,108,420. NMT is the exclusive licensee of this patent, which was issued to Dr. Marks in 1992.

In exchange for a cash payment of $30 million to NMT, AGA has been granted a nonexclusive sublicense to the patent involved in the litigation. The cash payment will be shared equally, after NMT’s legal fees and expenses, by NMT and Dr. Marks. All parties agreed to have the case dismissed with prejudice and also agreed to a general release of any and all claims.

“We are pleased to reach a favorable settlement and to have the long-running patent litigation concluded,” said NMT Medical President and Chief Executive Officer John E. Ahern. “Management is now in a better position to focus its energies on expanding its leadership in the emerging PFO (patent foramen ovale) closure market opportunity. The settlement will also provide us with additional flexibility to accelerate investments in our ongoing PFO closure clinical trials, new technology initiatives, and future sales and marketing programs.”

About NMT Medical, Inc.

NMT Medical is an advanced medical technology company that designs, develops, manufactures and markets proprietary implant technologies that allow interventional cardiologists to treat cardiac sources of migraine headaches, stroke and other potential brain attacks through minimally invasive, catheter-based procedures. NMT Medical is investigating the potential connection between a common cardiac defect called a PFO and brain attacks such as migraine headaches, stroke and TIAs. A PFO can allow venous blood, unfiltered and unmanaged by the lungs, to enter the arterial circulation of the brain, possibly triggering a cerebral event or brain attack. More than 20,000 PFOs have been closed globally with NMT’s minimally invasive, catheter-based implant technology.

The prevalence of migraines in the United States is about 10%. Of the 28 million migraine sufferers in America, those who experience aura and have a PFO may represent a three million patient subset. Stroke is the third leading cause of death in the United States and the leading cause of disability in adults. Each year, 750,000 Americans suffer a new or recurrent stroke and 500,000 Americans experience a TIA.

The Company also serves the pediatric interventional cardiologist with a broad range of cardiac septal repair implants delivered with nonsurgical catheter techniques. For more information about NMT Medical, please visit www.nmtmedical.com.

This press release contains “forward-looking statements” within the meaning of the Private Securities Litigation Reform Act of 1995. Such forward-looking statements — including statements regarding the effect of settlement with AGA Medical Corporation on the Company’s clinical trials and commercialization efforts — involve known and unknown risks, uncertainties or other factors which may cause actual results, performance or achievements of the Company to be materially different from any future results, performance or achievements expressed or implied by such forward-looking statements. Factors that may cause such a difference include, but are not limited to, the timing and ultimate outcome of any of the Company’s clinical trials, and the Company’s ability to develop and commercialize new products, potential delays in the regulatory process with the U.S. Food and Drug Administration and foreign regulatory agencies, as well as risk factors discussed under the heading “Certain Factors That May Affect Future Results” included in Management’s Discussion and Analysis of Financial Condition and Results of Operations in the Company’s Quarterly Report on Form 10-K for the year ended December 31, 2005 and subsequent filings with the U.S. Securities and Exchange Commission.