Exhibit 99.1

RAMTRON RESPONDS TO UNSOLICITED PROPOSAL

FROM CYPRESS SEMICONDUCTOR

Company to Explore Strategic Alternatives

Colorado Springs, CO – June 18, 2012 — Ramtron International Corporation (Nasdaq: RMTR), a leading developer and supplier of nonvolatile ferroelectric random access memory (F-RAM) and integrated semiconductor products, announced today that its Board of Directors has reviewed and carefully considered the unsolicited proposal dated June 12 from Cypress Semiconductor Corporation (Nasdaq: CY) with the assistance of its financial and legal advisors, and concluded that the proposal of $2.48 per share of common stock does not reflect the intrinsic value of the Company and is not in the best interest of Ramtron stockholders.

Ramtron also announced that its Board of Directors has authorized the exploration of strategic alternatives in the best interests of its stockholders. The Board intends to consider the full range of available options including, but not limited to, the potential sale of the Company or continuing with the Company’s current growth plans. Cypress has been invited to participate in this process.

“Under Eric Balzer’s leadership, Ramtron is a transformed company that is now poised to fully exploit the vast untapped opportunity for F-RAM-based low energy and high data integrity solutions in the semiconductor market,” said Dr. William G. Howard, Ramtron’s Chairman. “Over the past 18 months, he has assembled a world-class management team, successfully completed the foundry transition, resolved product supply shortages and implemented processes aimed at accelerating global adoption of F-RAM and enlarging the size of the Company’s addressable market. For the past three quarters, the Company has delivered positive net income and generated positive EBITDA. Having expanded capacity and addressed operational issues, the Company is intensely focused on delivering superior service to its customers and distributors and driving demand creation, and is gaining traction with its customer-centric sales and marketing initiatives and new product introductions.

“As a result, the Ramtron Board of Directors believes that Cypress’ unsolicited proposal fails to reflect the Company’s strengthened competitive position, F-RAM intellectual property and deep know-how, and strong prospects for long-term growth, as well as the progress being made toward expanding the Company’s product portfolio beyond specialty memory products to also include integrated semiconductor solutions,” concluded Dr. Howard.

RAMTRON RESPONDS TO UNSOLICITED PROPOSAL FROM CYPRESS SEMICONDUCTOR / Page 2

There can be no assurance that the exploration of strategic alternatives will result in any transaction. The Company does not intend to disclose developments regarding the exploration of strategic alternatives unless and until a transaction has been approved.

Needham & Company, LLC is serving as Ramtron’s financial advisor, and Shearman & Sterling LLP is serving as Ramtron’s legal advisor.

About Ramtron

Ramtron International Corporation, headquartered in Colorado Springs, Colorado, is a fabless semiconductor company that designs, develops and markets specialized semiconductor memory and integrated semiconductor solutions used in a wide range of product applications and markets worldwide. For more information, visit www.ramtron.com.

Additional Information

This communication does not constitute an offer to buy or solicitation of an offer to sell any securities. No tender offer for the shares of Ramtron International Corporation (“Ramtron”) has commenced at this time. If a tender offer is commenced, Ramtron may file a solicitation/recommendation statement on Schedule 14D-9 with the U.S. Securities and Exchange Commission (“SEC”). Any solicitation/recommendation statement filed by Ramtron that is required to be mailed to stockholders will be mailed to stockholders of Ramtron. INVESTORS AND STOCKHOLDERS OF RAMTRON ARE URGED TO READ THESE AND OTHER DOCUMENTS FILED WITH THE SEC CAREFULLY IN THEIR ENTIRETY IF AND WHEN THEY BECOME AVAILABLE BECAUSE THEY WILL CONTAIN IMPORTANT INFORMATION. Investors and stockholders will be able to obtain free copies of these documents (if and when available) and other documents filed with the SEC by Ramtron through the web site maintained by the SEC at http://www.sec.gov.

Cautionary Statements

Except for historical information, this press release contains forward-looking statements made pursuant to the safe harbor provisions of the Private Securities Litigation Reform Act of 1995. These statements may be identified by the use of forward-looking words or phrases such as “believe,” “expect,” “anticipate,” “should,” and “potential,” and “prospects”, among others as well as statements regarding the evaluation of strategic alternatives. These forward-looking statements are inherently difficult to predict and involve risks and uncertainties that could cause actual results to differ materially, including, but not limited to: general and regional economic conditions and conditions specific to the semiconductor industry; demand for Ramtron’s products; order cancellations or reduced order placements; product sales mix; the timely development of new technologies; competitive factors such as pricing pressures on existing products and the timing and market acceptance of new product introductions; Ramtron’s ability to maintain an appropriate amount of low-cost foundry production capacity from its foundry sources in a timely manner; our foundry partners’ timely ability to successfully manufacture products for Ramtron; our foundry partners’ ability to supply increased orders for F-RAM products in a timely manner using Ramtron’s proprietary technology; any disruptions of Ramtron’s foundry or test and assembly contractor relationships; currency fluctuations; unexpected design and manufacturing difficulties; defects in products that could result in product liability claims; risks and uncertainties relating to the possible transaction and process of exploring strategic alternatives; and the risk factors listed from time to time in Ramtron’s SEC reports, including, but not limited to, the Annual Report on Form 10-K for the year ended December 31, 2011 and the Quarterly Report on Form 10-Q for the quarter ended March 31, 2012. SEC-filed documents are available at no charge at the SEC’s website (www.sec.gov) or from the company.

All forward-looking statements included in this release are based upon information available to Ramtron as of the date of this release, which may change.

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