Draw true page border

You can use the crop package to place your pages on a A4 paper. It can center and frame it for you:

\documentclass{article}
\usepackage[paperwidth=16cm,paperheight=24cm]{geometry}
\usepackage[a4,frame,center]{crop}

\usepackage{lipsum}% dummy text
\begin{document}
\lipsum
\lipsum
\lipsum
\end{document}

It looks like this:

If you don't like the info line above the frame use the noinfo package option.

I had a similar issue with my own thesis. The way I dealt with it issue was to use features of the PDF format. PDF allows a file to specify several different boxes: TrimBox, MediaBox, ArtBox, CropBox, BleedBox. Relevant to this situation is MediaBox: the size of the paper you are printing on (in your case A4); and TrimBox: the size of the page after trimming. Many PDF viewers (Adobe Reader for example) are able to display these boxes optionally. I don't know of any packages that make use of this feature (would make a nice modification to geometry or crop), so I did it by hand: \pdfpageattr{/TrimBox[9 9 621 801]} where if I recall correctly the units are in pts. You can see a result here, where I wanted the final page to be US Letter size, but to have a 0.125" bleed before trimming. If you are using Adobe Reader, then to show the boxes use Edit -> Preferences -> Page Display -> Show art, trim, & bleed boxes.

If you are using geometry for setting the page parameters, then add the option showframe or showcrop