  We obtain constraints on quintessence models from magnitude-redshift
measurements of 176 type Ia Supernovae. The considered quintessence models are
ordinary quintessence, with Ratra-Peebles and SUGRA potentials, and extended
quintessence with a Ratra-Peebles potential. We compute confidence regions in
the $\Omega_{m0}-\alpha$ plane and find that for SUGRA potentials it is not
possible to obtain useful constraints on these parameters; for the
Ratra-Peebles case, both for the extended and ordinary quintessence we find
$\alpha\mincir 0.8$, at the $1\sigma$ level. We also consider simulated dataset
for the SNAP satellite for the same models: again, for a SUGRA potential it
will not be possible to obtain constraints on $\alpha$, while with a
Ratra-Peebles potential its value will be determined with an error $\mincir
0.6$. We evaluate the inaccuracy made by approximating the time evolution of
the equation of state with a linear or constant $w\diz$, instead of using its
exact redshift evolution. Finally we discuss the effects of different
systematic errors in the determination of quintessence parameters.
