Conference. The Free Dictionary says:
a meeting for consultation or discussion: a conference between a
student and her adviser (Emphasis added)
In other definitions, a conference is described as "a formal meeting...", and the OP wanted a formal word. Etymonline says, for conference:
1550s, "act of conferring," from Middle French conférence (15c.), from
Medieval Latin conferentia, from Latin conferens, present participle
of conferre "to bring together; deliberate, talk over" (see confer).
Meaning "formal meeting for consultation" is from 1580s.
The word gives more status to the student than words that imply that you, the advisor, are checking up on the student. The student is more of an equal participant in a conference, and, if this is a research project, she may have information or insights that are new to you.
A conference often involves many people, but does not have to: You can confer with one other person, and have a conference with one other person. Merriam-Webster on conference:
a meeting of two or more persons for discussing matters of common
Example: He spent an hour in conference with the president