When preparing for her first U.S. Supreme Court argument in United States v. Windsor, Roberta Kaplan faced “something like seven moot courts,” she recalled last week. “It was like a root canal without anesthesia.”

Two of the four lawyers who will make their high court debuts this month in the same-sex marriage challenges no doubt are discovering what Kaplan, an experienced appellate litigator at Paul, Weiss, Rifkind, Wharton & Garrison, learned in 2013: A Supreme Court argument is in a category by itself.