  We prove two new approximation results of $H$-perimeter minimizing boundaries
by means of intrinsic Lipschitz functions in the setting of the Heisenberg
group $\mathbb{H}^n$ with $n\ge2$. The first one is an improvement of a result
of Monti and is the natural reformulation in $\mathbb{H}^n$ of the classical
Lipschitz approximation in $\mathbb{R}^n$. The second one is an adaptation of
the approximation via maximal function developed by De Lellis and Spadaro.
