Let $\mathcal P_n$ be the class of algebraic polynomials $P(x)=\sum_{v=0}^{n}a_vx^v$ of degree at most $n$ and $\|P\|_{d\sigma}=(\int_{\mathbb R}|P(x)|^2d\sigma(x))^{1/2}$, where $d\sigma(x)$ is a nonnegative measure on $\mathbb R$. We consider the best constant in the inequality $|a_v|\leq C_{n,v}(d\sigma)\|P\|_{d\sigma}$, when $P\in\mathcal P_n$ and such that $P(\xi_k)=0$ $(k=1,2,\ldots,m)$. The cases $C_{n,n}(d\sigma)$ and $C_{n,n-1}(d\sigma)$ were studied by Milovanović and Guessab [2] and for an arbitrary $v$ by Milovanović and Rančić [5], where they gave explicit expressions for some classical measures. In this paper we determine the best constants $C_{n,v}$ for the generalized Gegenbauer measure on $(-1,1)$ and for the generalized Hermite measure on $(-\infty,+\infty)$.