  The norms or expectation values of infinite projected entangled-pair states
(PEPS) cannot be computed exactly, and approximation algorithms have to be
applied. In the last years, many efficient algorithms have been devised -- the
corner transfer matrix renormalization group (CTMRG) and variational uniform
matrix product state (VUMPS) algorithm are the most common -- but it remains
unclear whether they always lead to the same results. In this paper, we
identify a subclass of PEPS for which we can reformulate the contraction as a
variational problem that is algorithm independent. We use this variational
feature to assess and compare the accuracy of CTMRG and VUMPS contractions.
Moreover, we devise a new variational contraction scheme, which we can extend
to compute general N-point correlation functions.
