Likely Costa's highest-profile prosecution in his six years as a federal prosecutor has been the case against alleged Ponzi schemer Allen Stanford, who was indicted in 2009. In January 2011, Stanford's legal team requested a delay of the start of his scheduled January 24, 2011 trial, noting that they had only taken over his defense in October 2010. Costa told the judge presiding over the trial that while he did not object to some delay in the trial, "the requested continuance of two years is excessive." In February 2011, Stanford sued Costa and his fellow prosecutor Paul Pelletier, along with several employees of the Securities and Exchange Commission and the Federal Bureau of Investigation, complaining of "abusive law enforcement" and seeking $7.2 billion in damages. In March 2011, Stanford's attorneys argued that the defendant's right to a speedy trial had been violated. Costa, however, told the Associated Press that delays largely were the result of Stanford's own requests for continuances. In March 2012, Stanford was found guilty on 13 of 14 counts including fraud, obstructing investigators and conspiracy to commit money laundering.
Federal judicial service
Service on the U.S. District Court for the Southern District of Texas
In July 2011, Texas's two Republican senators, John Cornyn and Kay Bailey Hutchison, sent a letter to President Barack Obama, recommending that he nominate Costa to the vacant seat on the United States District Court for the Southern District of Texas that had been created when Judge John David Rainey took senior status in June 2010. The seat would be based in the Galveston Division. The anticipated nomination earned bipartisan support, as Democratic United States RepresentativeLloyd Doggett, who serves as the spokesman for Texas Democrats on federal judicial matters, urged the president to nominate Costa as well. On September 8, 2011, President Obama nominated Costa to the seat on the U.S. District Court for the Southern District of Texas. He received a hearing by the Senate Judiciary Committee on November 2, 2011, and his nomination was reported to the floor on December 1, 2011. Costa's nomination was approved by the U.S. Senate on April 26, 2012, by a 97–2 vote and he received his commission the same day.
On December 19, 2013 President Obama nominated Judge Costa to a vacant seat on the U.S. Court of Appeals for the Fifth Circuit due to Fortunato Benavides assuming senior status. He received a hearing before the U.S. Senate Judiciary Committee on February 25, 2014. On March 27, 2014, Costa's nomination was reported out of committee by voice vote. On May 13, 2014, Senate Majority LeaderHarry Reid filed for cloture on Costa's nomination. On Thursday May 15, 2014 the Senate voted 58–36 on the motion to invoke cloture. On Tuesday, May 20, 2014 the Senate voted 97–0 for final confirmation and elevation to the U.S. Court of Appeals for the Fifth Circuit. He was commissioned as a judge for the Fifth Circuit on June 2, 2014.