Let $m,s \in \mathbb{R}$, let $0<h_0 \leq 1$, and let $a = a(x,\xi;h)$ be a semiclassical symbol family in $S^m(T^*\mathbb{R}^n)$ for $0<h\leq h_0$. For multi-indices $\alpha,\beta \in \mathbb{N}_0^n$, define the symbol seminorm
interpreted as an oscillatory integral for $u\in\mathcal{S}(\mathbb{R}^n)$. Then for every $s\in\mathbb{R}$ there exist an integer $N=N(n,m,s)$ and a constant $C=C(n,m,s,h_0)>0$ such that, for every $0<h\leq h_0$ and every $u\in\mathcal{S}(\mathbb{R}^n)$,