An inner nuncial series was a special kind of deep medical scan that couldn't be performed by a medical tricorder but instead had to be done in a sickbay.

Doctor Beverly Crusher performed an inner nuncial series on Deanna Troi in order to find out why she had lost her empathic senses in 2367. (TNG: "The Loss")

The Star Trek Encyclopedia (4th ed., vol. 1, p. 364) described "inner nuncial series" as a battery of neurological tests.