Single caption and (a) and (b) with the tabular within tabular
solution is one way.  I.e.,

\begin{figure}
\begin{tabular}{ccc}
\input figure1stuff&~~&\input figure2stuff\\
(a)&&(b)
\end{tabular}
\caption{(a) Figure 1, and (b) Figure 2.}\label{f1andf2}
\end{figure}

It should be possible to replace (a) and (b) with
\protect\caption{Figure...}.

Another solution is to place each figure within a minipage

\begin{figure}
\begin{minipage}{0.4\textwidth}
figure 1
\caption{1}\label{f1}
\end{minipage}\hspace{\fill}
\begin{minipage}{0.4\textwidth}
figure 2
\caption{2}\label{f2}
\end{minipage}
\end{figure}