  Although micro-lensing of macro-lensed quasars and supernovae provides unique
opportunities for several kinds of investigations, it can add unwanted and
sometimes substantial noise. While micro-lensing flux anomalies may be safely
ignored for some observations, they severely limit others. "Worst-case"
estimates can inform the decision whether or not to undertake an extensive
examination of micro-lensing scenarios. Here, we report "worst-case"
micro-lensing uncertainties for point sources lensed by singular isothermal
potentials, parameterized by a convergence equal to the shear and by the
stellar fraction. The results can be straightforwardly applied to
non-isothermal potentials utilizing the mass sheet degeneracy. We use
micro-lensing maps to compute fluctuations in image micro-magnifications and
estimate the stellar fraction at which the fluctuations are greatest for a
given convergence. We find that the worst-case fluctuations happen at a stellar
fraction $\kappa_\star=\frac{1}{|\mu_{macro}|}$. For macro-minima, fluctuations
in both magnification and demagnification appear to be bounded ($1.5>\Delta
m>-1.3$, where $\Delta m$ is magnitude relative to the average
macro-magnification). Magnifications for macro-saddles are bounded as well
($\Delta m > -1.7$). In contrast, demagnifications for macro-saddles appear to
have unbounded fluctuations as $1/\mu_{macro}\rightarrow0$ and
$\kappa_\star\rightarrow0$.
