How can I draw a horizontal round parenthesis above some text? How do I specify a round parenthesis below some text? explains how to do it below text.
1 Answers
The abraces package under the overload package option provides this when using \overbrace[L1R] or \underbrace[l1r]:

\documentclass{article}
\usepackage[overload]{abraces}% http://ctan.org/pkg/abraces
\begin{document}
$\overbrace[L1R]{\textrm{The quick brown fox jumped over the lazy dog}}$ \par \medskip
$\underbrace[l1r]{\textrm{The quick brown fox jumped over the lazy dog}}$ \par
\end{document}
Original answer:
Here is a modified version of \overbrace in the form of \overfence, which should provide what you're after.

\documentclass{article}
\usepackage{mathtools}% http://ctan.org/pkg/mathtools
\usepackage{etoolbox}% http://ctan.org/pkg/etoolbox
% \overfence definition
\let\overfence\overbrace % \overfence is similar to \overbrace
\let\downfencefill\downbracefill % match components of \overbrace
\patchcmd{\overfence}{\downbracefill}{\downfencefill}{}{}% patch \overfence...
\patchcmd{\downfencefill}{\braceru \bracelu}{}{}{}%... and \downfencefill
% \underfence definition
\let\underfence\underbrace % \underfence is similar to \underbrace
\let\upfencefill\upbracefill % match components of \underbrace
\patchcmd{\underfence}{\upbracefill}{\upfencefill}{}{}% patch \underfence...
\patchcmd{\upfencefill}{\bracerd \braceld}{}{}{}%... and \upfencefill
\begin{document}
$\overbracket{\textrm{The quick brown fox jumped over the lazy dog}}$ \par
$\overbrace{\textrm{The quick brown fox jumped over the lazy dog}}$ \par
$\overfence{\textrm{The quick brown fox jumped over the lazy dog}}$ \par \medskip
$\underbracket{\textrm{The quick brown fox jumped over the lazy dog}}$ \par
$\underbrace{\textrm{The quick brown fox jumped over the lazy dog}}$ \par
$\underfence{\textrm{The quick brown fox jumped over the lazy dog}}$
\end{document}
In fact, since \overfence duplicates the behaviour of \overbrace, you can even add stuff to it since it's typeset as a \mathop with \limits. For example:

$\overfence{\textrm{The quick brown fox jumped over the lazy dog}}^{\mbox{\scriptsize Because the dog is really lazy.}}$