  In this paper, we study the existence and concentration of normalized
solutions to the supercritical nonlinear Schr\"{o}dinger equation
\begin{equation*} \left\{ \begin{array}{l} -\Delta u + V(x) u = \mu_q u +
a|u|^q u \quad {\rm in}\quad \mathbb{R}^2,\\ \int_{\mathbb{R}^2}|u|^2\,dx =1,\\
\end{array} \right. \end{equation*} where $\mu_q$ is the Lagrange multiplier.
For ellipse-shaped potentials $V(x)$, we show that for $q>2$ close to $2$, the
equation admits an excited solution $u_q$, and furthermore, we study the
limiting behavior of $u_q$ when $q\to 2_+$. Particularly, we describe precisely
the blow-up formation of the excited state $u_q$.
