You can simplify your code:
using System.Linq
private void getIntersection(Panel targetPanel, Control containerToSearch)
{
Rectangle targetBounds = targetPanel.Bounds;
Rectangle testIntersect;
foreach (Panel thePanel in containerToSearch.Controls.OfType<Panel>())
{
if (thePanel == targetPanel) continue;
testIntersect = Rectangle.Intersect(targetBounds, thePanel.Bounds);
if (testIntersect != Rectangle.Empty)
{
Console.WriteLine("panel name: {0} \r\nintersection: {1}", thePanel.Name, testIntersect.ToString());
break;
}
}
}</panel>