  We investigate the possibility of measuring the Hubble constant, the
fractional energy density components and the equation of state parameter of the
``dark energy'' using lensed multiple images of high-redshift supernovae. With
future instruments, such as the SNAP and NGST satellites, it will become
possible to observe several hundred lensed core-collapse supernovae with
multiple images. Accurate measurements of the image separation, flux-ratio,
time-delay and lensing foreground galaxy will provide complementary information
to the cosmological tests based on, e.g., the magnitude-redshift relation of
Type Ia supernovae, especially with regards to the Hubble parameter that could
be measured with a statistical uncertainty at the one percent level. Assuming a
flat universe, the statistical uncertainty on the mass density is found to be
sigma^stat_m <0.05. However, systematic effects from the uncertainty of the
lens modeling are likely to dominate. E.g., if the lensing galaxies are
extremely compact but are (erroneously) modeled as singular isothermal spheres,
the mass density is biased by sigma^syst_m =0.1.
  We argue that wide-field near-IR instruments such as the one proposed for the
SNAP mission are critical for collecting large statistics of lensed supernovae.
