In late February, three weeks after she had an operation for a recurrence of cancer, Justice Ruth Bader Ginsburg went to Barack Obama’s first address to Congress. Given the circumstances, it wasn’t an event anyone expected her to attend. She went, she said, because she wanted the country to see that there was a woman on the Supreme Court.

Now another woman, Judge Sonia Sotomayor, is about to begin the confirmation hearings that stand between her and a seat near Ginsburg on the high bench. After 16 years on the court — the last three, since the retirement of Justice Sandra Day O’Connor, as the only woman working alongside eight men — Ginsburg has a unique perspective on what’s at stake in Sotomayor’s nomination. I sat down with the...