  The precise determination of the leptonic $CP$-phase is one of the major
goals for future generation long Baseline experiments. On the other hand, if
new physics beyond the Standard Model exists, a robust determination of such a
$CP$-phase may be a challenge. Moreover, it has been pointed out that, in this
scenario, an apparent discrepancy in the $CP$-phase measurement at different
experiments may arise. In this work, we investigate the determination of the
Dirac $CP$-phase and the atmospheric mixing angle $\theta_{23}$ at several
long-baseline configurations: ESSnuSB, T2HKK, and a DUNE-like experiment. We
use the nonstandard neutrino interactions (NSI) formalism as a framework. We
found that complementary between ESSnuSB and a DUNE-like experiment will be
favorable to obtain a reliable value of the $CP$-phase, within the
aforementioned scenario. Moreover, the T2HKK proposal can help to constrain the
matter NSI parameters.
