What are the connotations of "Lo Sa'aneh ... Eid Shav"?
Ramban: "Eid Shav" - as opposed to "Eid Shaker"
- means a 'vain testimony, which will not cause the relevant litigant a loss in Beis-Din.
Such as where the witness testifies that Reuven undertook to give Shimon a Manah without making a Kinyan. See also R. Chavel's footnotes.