  We establish robust exponential convergence for $rp$-Finite Element Methods
(FEMs) applied to fourth order singularly perturbed boundary value problems, in
a \emph{balanced norm} which is stronger than the usual energy norm associated
with the problem. As a corollary, we get robust exponential convergence in the
maximum norm. $r p$ FEMs are simply $p$ FEMs with possible repositioning of the
(fixed number of) nodes. This is done for a $C^1$ Galerkin FEM in 1-D, and a
$C^0$ mixed FEM in 2-D over domains with smooth boundary. In both cases we
utilize the \emph{Spectral Boundary Layer} mesh.
