Changing color is not really supported, so you lose some metric information and a manual correction could be needed in some cases:
\documentclass{article}
\usepackage{mathtools,xcolor}
\newcommand{\colorwt}[2][2]{%
{}\mspace{#1mu}\mathrlap{\textcolor{red}{\widetilde{\phantom{#2}}}}%
\mspace{-#1mu}#2%
}
\begin{document}
X$\widetilde{E}^{w}$X$\widetilde{I}$X
X$\colorwt{E}^{w}$X$\colorwt{I}$X
X$\colorwt[3]{E}^{w}$X$\colorwt[3]{I}$X
X$\colorwt[2]{E}^{w}$X$\colorwt[2]{I}$X
X$\colorwt[1]{E}^{w}$X$\colorwt[1]{I}$X
\end{document}
The default value of the manual correction is 2, I have shown what's the effect when you specify a different value.

wwas not close enough toE. – Bernard Jun 23 '14 at 09:59