From Boston Globe - NEW ENGLAND IN BRIEF, April 28, 2005:

SJC arguments will be shown online

Want to see the state's highest court in action without leaving your desk? If you have Internet access, you can do so starting on Monday [May 2], when Massachusetts will join about a dozen other states whose top courts broadcast oral arguments live on the Web. In a pilot project undertaken with Suffolk University Law School, the Supreme Judicial Court will begin webcasting oral arguments when the seven justices hold their May session next week. The gavel-to-gavel action can be viewed starting at 9 a.m. each day at www.suffolk.edu/sjc. One of the first cases to be broadcast on Monday will be a request by the executive director of the Catholic Action League of Massachusetts for the court to set aside its landmark ruling legalizing same-sex marriage.

That case is: SJC-09254: Doyle v. Goodrich:

Same-sex Marriage — This case deals with whether a citizen has standing to seek to stay the judgment in Goodridge v. Department of Public Health during the pendency of the process to amend the Massachusetts Constitution.

See also massdems.org: Catholic Action League on the SJC Ruling