  We obtain precise plateau estimates for the two-point function of the
finite-volume weakly-coupled hierarchical $|\varphi|^4$ model in dimensions $d
\ge 4$, for both free and periodic boundary conditions, and for any number $n
\ge 1$ of components of the field $\varphi$. We prove that, within a critical
window around their respective effective critical points, the two-point
functions for both free and periodic boundary conditions have a plateau, in the
sense that they decay as $|x|^{-(d-2)}$ until reaching a constant plateau value
of order $V^{-1/2}$ (with a logarithmic correction for $d=4$), where $V$ is
size of the finite volume. The two critical windows for free and periodic
boundary conditions do not overlap. The dependence of the plateau height on the
location within the critical window is governed by an explicit $n$-dependent
universal profile which is independent of the dimension. The proof is based on
a rigorous renormalisation group method and extends the method used by Michta,
Park and Slade (arXiv:2306.00896) to study the finite-volume susceptibility and
related quantities. Our results lead to precise conjectures concerning
Euclidean (non-hierarchical) models of spin systems and self-avoiding walk in
dimensions $d \ge 4$.
