I have searched around for this but couldn't figure out the solution for my particular document.
Using this answer I have placed two images of different width side by side.
I would like the text of image (a) to not wrap. Ideally, I would like the image to be centered above the non-wrapped caption.
MWE
\documentclass{article}
\usepackage{graphicx}
\usepackage{subfig}
\begin{document}
\newsavebox{\myimage}
\begin{figure}
\centering
\savebox{\myimage}{\hbox{\rule{150pt}{150pt}}}% Store largest image
\subfloat[First caption text is a bit longer and wraps.]{\usebox{\myimage}} \quad
\subfloat[Second fits on one line.]{\raisebox{\dimexpr.5\ht\myimage-.5\height\relax}{\rule{100pt}{20pt}}}
\caption{This is a figure.}
\end{figure}
\end{document}

