I believe I understand your dilemma and I have something for you to try. I faced the same issue and this worked for me.
Add a script to your search page:
<SCRIPT language="javascript">function popWin() {
FormResults=window.open("","FormResults","");
}
</SCRIPT>
Modify your search form along the lines below. I used an image type instead of a button, but it doesn't matter. Hope this helps.
<FORM method="GET" action="http://whatever.com/file.php" target="FormResults">
<INPUT type=image name="click to search" onclick="popWin()" src="cool.gif" border="0" width="57" height="20" align="left" alt="click to search">
etc ...