  We analyse the constraints that can be placed on a cosmological constant or
quintessence-like component by combining observations of Type Ia supernovae
with measurements of anisotropies in the cosmic microwave background. We use
the recent supernovae sample of Perlmutter et al and observations of the CMB
anisotropies to constraint the equation of state (w_Q = p/rho) in
quintessence-like models via a likelihood analysis. The 2 sigma upper limits
are w_Q < -0.6 if the Universe is assumed to be spatially flat, and w_Q < -0.4
for universes of arbitrary spatial curvature. The upper limit derived for a
spatially flat Universe is close to the lower limit (w_Q approx -0.7) allowed
for simple potentials, implying that additional fine tuning may be required to
construct a viable quintessence model.
