In this work we examine a posteriori error control for post-processed
approximations to elliptic boundary value problems. We introduce a class of
post-processing operator that `tweaks' a wide variety of existing
post-processing techniques to enable efficient and reliable a posteriori bounds
to be proven. This ultimately results in optimal error control for all manner
of reconstruction operators, including those that superconverge. We showcase
our results by applying them to two classes of very popular reconstruction
operators, the Smoothness-Increasing Accuracy-Enhancing filter and
Superconvergent Patch Recovery. Extensive numerical tests are conducted that
confirm our analytic findings.Comment: 25 pages, 17 figure