  Self-testing has been established as a major approach for quantum device
certification based on experimental statistics under minimal assumptions.
However, despite more than 20 years of research effort most of the self-testing
protocols are restricted to spatial scenarios (Bell scenarios), without any
temporal generalisations known. Under the scenario of sequential measurements
performed on a single quantum system, we build upon previous works which used
semi-definite programming (SDP) based methods to bound sequential measurement
inequalities. For such SDPs, we show that the optimiser matrix is unique and
moreover this uniqueness is robust to small deviations from the quantum bound.
Further, we consider a generalised scenario in presence of quantum channels and
draw analogies in the structure of Bell and sequential inequalities using the
pseudo-density matrix formalism. These analogies allow us to show a practical
use of maximal violations of sequential inequalities in the form of
certification of quantum channels up to isometries.
