Non obstante veredicto refers to a type of judgment that can be given at the end of a jury trial. Specifically, a lawyer would ask for a non obstante veredicto when the lawyer believes that a reasonable jury could not come up with the judgment that the actual jury came up with.
Non obstante veredicto is better known as a judgment notwithstanding the verdict (JNOV).
A non obstante veredicto is very rarely granted. For a judge to grant it, the judge must find that the jury did not follow the instructions given by the court.