The main result of this paper are novel two-sided estimates of the essential resolvent norm for closed linear operators T . We prove that the growth of \|(T-\lambda)^{-1}\|_{\textup{e}} is governed by the distance of a point \lambda\in{}\rho(T){}\setminus{}W_{\textup{e}}(T) to the essential numerical range W_{\textup{e}}(T) . We extend these bounds even to points \lambda{}\in \mathbb{C}\setminus W_{\textup{e}}(T) outside the resolvent set \rho(T) with (T{}-{}\lambda)^{-1} replaced by the Moore–Penrose resolvent (T-\lambda)^{\dagger}{} . We use similar ideas to prove essential growth bounds in terms of the real part of the essential numerical range of generators of C_{0} -semigroups. Further, we study the essential approximate point spectrum \sigma_{{\textup{eap}}}(T) and the essential minimum modulus \gamma_{\textup{e}}(T) , in particular, their relations to the various essential spectra and the essential norm of the Moore–Penrose inverse, respectively. An important consequence of our results are new perturbation results for the spectra and essential spectra (of type 2) for accretive and sectorial T . Applications e.g. to Schrödinger operators with purely imaginary rapidly oscillating potentials in \mathbb{R}^{d} illustrate our results.