We investigate the uniform convergence of Lagrange interpolation at the zeros of Hermite polynomials in the presence of constraints. We show that by a simple procedure it is always possible to transform the matrices of these zeros into matrices such that the corresponding Lagrange interpolating polynomial with respect to the given constraints well approximates a given function. This procedure was, at first, successfully introduced for the polynomial interpolation with constraints on bounded intervals [1]. For this procedure we obtain the same results obtained in [2], where only the zeros of the Hermite polynomial are used.