  For nonnegative even kernels $K$, we consider the $K$-nonlocal perimeter
functional acting on sets. Assuming the existence of a foliation of space made
of solutions of the associated $K$-nonlocal mean curvature equation in an open
set $\Omega\subset\mathbb{R}^n$, we built a calibration for the nonlocal
perimeter inside $\Omega\subset\mathbb{R}^n$. The calibrating functional is a
nonlocal null-Lagrangian. As a consequence, we conclude the minimality in
$\Omega$ of each leaf of the foliation. As an application, we prove the
minimality of $K$-nonlocal minimal graphs and that they are the unique
minimizers subject to their own exterior data.
  As a second application of the calibration, we give a simple proof of an
important result from the seminal paper of Caffarelli, Roquejoffre, and Savin,
stating that minimizers of the fractional perimeter are viscosity solutions.
