  Despite the success of the combination of conservative schemes and staggered
constrained transport algorithms in the last fifteen years, the accurate
description of highly magnetized, relativistic flows with strong shocks
represents still a challenge in numerical RMHD. The present paper focusses in
the accuracy and robustness of several correction algorithms for the conserved
variables, which has become a crucial ingredient in the numerical simulation of
problems where the magnetic pressure dominates over the thermal pressure by
more than two orders of magnitude.
  Two versions of non-relativistic and fully relativistic corrections have been
tested and compared using a magnetized cylindrical explosion with high
magnetization ($ \ge 10^4$) as test. In the non-relativistic corrections, the
total energy is corrected for the difference in the classical magnetic energy
term between the average of the staggered fields and the conservative ones,
before (CA1) and after (CA1') recovering the primitive variables. These
corrections are unable to pass the test at any numerical resolution. The two
relativistic approaches (CA2 and CA2'), correcting also the magnetic terms
depending on the flow speed in both the momentum and the total energy, reveal
as much more robust. These algorithms pass the test succesfully and with very
small deviations of the energy conservation ($\le 10^{-4}$), and very low
values of the total momentum ($\le 10^{-8}$). In particular, the algorithm CA2'
(that corrects the conserved variables after recovering the primitive
variables) passes the test at all resolutions.
  The numerical code used to run all the test cases is briefly described.
