  We prove a sharp resolvent estimate in scale invariant norms of
Amgon--H\"{o}rmander type for a magnetic Schr\"{o}dinger operator on
$\mathbb{R}^{n}$, $n\ge3$\begin{equation*} L=-(\partial+iA)^{2}+V
\end{equation*}with large potentials $A,V$ of almost critical decay and
regularity.
  The estimate is applied to prove sharp smoothing and Strichartz estimates for
the Schr\"{o}dinger, wave and Klein--Gordon flows associated to $L$.
