Experiments on tetragonal Sr2RUO4 and CeIrIn5 indicate the presence of supe
rconductivity with a multicomponent superconducting order parameter. Such a
n order parameter should exhibit an in-plane anisotropy in the upper critic
al field near the superconducting transition temperature that does not occu
r for single-component superconductors. Here, this anisotropy is determined
from microscopic calculations for arbitrary gap functions. It is shown tha
t this anisotropy is generally not small and, in some cases, independent of
impurity scattering, Furthermore, this anisotropy is calculated for many d
etailed microscopic models of Sr2RuO4. For these models this anisotropy is
found to be large, which is in sharp contrast to the small anisotropy obser
ved experimentally. However, an accidental cancellation of the anisotropy f
or gape, on different Fermi surface sheets can lead to a result that is con
sistent with experiment.