To evaluate the function \( f(x) = -x^2 - 4 \) for \( x = -3 \), we substitute \(-3\) for \(x\) in the function:
\[ f(-3) = -(-3)^2 - 4 \]
Now, calculate \((-3)^2\):
\[ (-3)^2 = 9 \]
Then, substitute this value into the function:
\[ f(-3) = -9 - 4 \]
Now combine the terms:
\[ f(-3) = -9 - 4 = -13 \]
Thus, the value of \( f(-3) \) is \(-13\).
Therefore, the answer is:
\[ \boxed{-13} \]