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 $kappa_starrightarrow0$.
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