  Several correlations among Gamma Ray Burst (GRB) observables with available
redshifts have been recently identified. Proper evaluation and calibration of
these correlations may facilitate the use of GRBs as standard candles
constraining the expansion history of the universe up to redshifts of $z>6$.
Here we use the 69 GRB dataset recently compiled by Schaefer (astro-ph/0612285)
and we test the calibration of five of the above correlations
($1:\epkk-E_\gamma$, $2:\epkk-L$, $3:\tlag-L$, $4:V-L$, $5:\trt-L$) with
respect to two potential sources of systematics: Evolution with redshift and
cosmological model used in the calibration. In examining the model dependence
we assume flat \lcdm and vary $\omm$. Our approach avoids the circularity
problem of previous studies since we do not fix $\omm$ to find the correlation
parameters. Instead we simultaneously minimize $\chi^2$ with respect to both
the log-linear correlation parameters $a$, $b$ and the cosmological parameter
$\omm$. We find no statistically significant evidence for redshift dependence
of $a$ and $b$ in any of the correlation relations tested. We also find that
one of the five correlation relations tested ($\epkk-E_\gamma$) has a
significantly lower intrinsic dispersion compared to the other correlations.
For this correlation relation, the maximum likelihood method favors the
existence of a cosmological constant while the other four correlation favor a
flat matter dominated universe $\omm \simeq 1$. Finally, a cross-correlation
analysis between the GRBs and SnIa data for various values of $\omm$ has shown
that the $E_{peak}-E_\gamma$ relation traces well the SnIa redshift regime.
However, even the tightest correlation relation ($E_{peak}-E_\gamma$) provides
much weaker constraints on $\omm$ than current SnIa data.
