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It’s unclear what will happen in the case. But Evan Wolfson, president of Freedom to Marry, lauded Ms. Baldwin and Ms. Bishop for their persistence.

“Whatever the wisdom of a particular litigation in a particular state in the midst of a national movement for the freedom to marry, couples like Mary and Sharon who have gone the full mile to walk down the aisle attest to the undeniable fact that marriage matters, for gay couples as for non-gay,” Mr. Wolfson said.

• Associated Press writer David Crary contributed to this report from New York.