Accent commands (e.g. \'e) don't work in a tabbing environments

It is described in manuals to LaTeX that inside tabbing you have to use \a'{e} instead of \'{e}. This will work for you. As well, I recommend loading lmodern and [T1]{fontenc} to get proper accent placement:

\documentclass{article}
\usepackage{lmodern}
\usepackage[T1]{fontenc}
\begin{document}
\section{EDUCATION \& CERTIFICATION}
\begin{tabbing}
\textbf{Imperial College}, London, UK \= \hspace{1.6in} \= Sep 2013 \\
Master in Economics \\[2ex]
\textbf{Ecole Sup\a'erieure}, Paris, France \> \> Sep 2012 \\
Master of Sciences\\[2ex]
\bf{Ecole Sup\a'erieure}, Paris, France \> \> Sep 2012 \\
Master of Sciences\\[2ex]
Ecole Sup\a'erieure, Paris, France \> \> Sep 2012 \\
Master of Sciences\\[2ex]
\textbf{Ecole Sup\a'{e}rieure}, Paris, France \> \> Sep 2012 \\
Master of Sciences\\[2ex]
\end{tabbing}
\end{document} 

You can use

\usepackage[utf8]{inputenc}

in order to simply have to type the accents. That means that you don't have to code \a'{e}, but that you can directly type é. I'm not sure whether this is very helpful or not, but in my opinion, this is a lot faster solution.