jmc

Dividing $-100$ by $9$ gives $-11$ with a remainder of $-1$. In other words, $$-100=-11\cdot 9+(-1).$$This means that $-11\cdot 9=-99$ is greater than $-100$. Because the negation of $99$ is $-99$, $\boxed{99}$ is the largest multiple of $9$ whose negation is greater than $-100$.

We could also divide $-100$ by $9$ to get $-12$ with a positive remainder of $11$. However, $-12\cdot 9$ is less than $-100$, so $$-100=-12\cdot 9+11$$would not help.