Look for a bigger delimiter than \Bigg

You could scale / using \scalebox{<factor>}{<stuff>} from the graphicx package:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\usepackage{graphicx}% http://ctan.org/pkg/graphicx
\begin{document}
\[\left.
  \begin{vmatrix}
    a_{11}&a_{12}&a_{13}\\
    a_{21}&a_{22}&a_{23}\\
    a_{31}&a_{32}&a_{33}
  \end{vmatrix}\middle/\begin{vmatrix}
    b_{11}&b_{12}&b_{13}\\
    b_{21}&b_{22}&b_{23}\\
    b_{31}&b_{32}&b_{33}\\
    b_{41}&b_{42}&b_{43}
  \end{vmatrix}
\right.\]
\[
  \begin{vmatrix}
    a_{11}&a_{12}&a_{13}\\
    a_{21}&a_{22}&a_{23}\\
    a_{31}&a_{32}&a_{33}
  \end{vmatrix}\scalebox{1.5}{\Bigg/}\begin{vmatrix}
    b_{11}&b_{12}&b_{13}\\
    b_{21}&b_{22}&b_{23}\\
    b_{31}&b_{32}&b_{33}\\
    b_{41}&b_{42}&b_{43}
  \end{vmatrix}
\]
\end{document}

Note that this scales / both vertically and horizontally, increasing the width of the symbol as well. To minimize this, I've only scaled \Bigg/. To see the difference, consider (say) \raisebox{-2ex}{\scalebox{4.5}{/}}.

Another alternative could be to rotate a vertical rule by (say) 15 degrees clockwise. For this you could use

\rotatebox{-15}{\rule[-1.8\baselineskip]{0.4pt}{4\baselineskip}}

The above vertical rule has a fixed width of 0.4pt, which you can change to your liking.

If you have access to the mtpro2 package (short for "MathTime Pro II"), you can use the following code

\documentclass{article}
\usepackage[lite]{mtpro2} % note: only "lite" subset of the mtpro2 package is needed
\usepackage{amsmath}
\begin{document}
\[
  \PARENS{\begin{matrix}
    a_{11}&a_{12}&a_{13}\\
    a_{21}&a_{22}&a_{23}\\
    a_{31}&a_{32}&a_{33}
  \end{matrix}}
  \LEFTRIGHT/.{\PARENS{\begin{matrix}
    b_{11}&b_{12}&b_{13}\\
    b_{21}&b_{22}&b_{23}\\
    b_{31}&b_{32}&b_{33}\\
    b_{41}&b_{42}&b_{43}
  \end{matrix}}}
\]
\end{document}

to produce this output:

The package's documentation states that delimiters produced with the \LEFTRIGHT<a><b> command (where the left and right hand symbols "a" and "b" can be different) can be up to 10 cm (4") tall. As shown in the example, if you need a "delimiter" on only one side, you should use a "." symbol for the other delimiter.

The full mtpro2 package is not free. However, the so-called "lite" subset of this package is indeed free of charge and may be downloaded from this website.

The only problem is that there is no so big slash in the font. If you use \middle| or \middle( instead, the delimiter will be big enough.

If necessary, scaling as what Werner do, or use a drawing package like tikz may help.

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}

\begin{document}
\[
\begin{vmatrix}
a_{11}&a_{12}&a_{13}\\
a_{21}&a_{22}&a_{23}\\
a_{31}&a_{32}&a_{33}
\end{vmatrix}
\tikz[baseline]\draw(-1em,-2\baselineskip)--(1em,2\baselineskip);
\begin{vmatrix}
b_{11}&b_{12}&b_{13}\\
b_{21}&b_{22}&b_{23}\\
b_{31}&b_{32}&b_{33}\\
b_{41}&b_{42}&b_{43}
\end{vmatrix}
\]

\end{document}