  We study spectral stability of the $\bar\partial$-Neumann Laplacian on a
bounded domain in $\mathbb{C}^n$ when the underlying domain is perturbed. In
particular, we establish upper semi-continuity properties for the variational
eigenvalues of the $\bar\partial$-Neumann Laplacian on bounded pseudoconvex
domains in $\mathbb{C}^n$, lower semi-continuity properties on pseudoconvex
domains that satisfy property ($P$), and quantitative estimates on smooth
bounded pseudoconvex domains of finite D'Angelo type in $\mathbb{C}^n$.
