Very much did not like having to hover over just the bare border of the control. I fisgured out a better way:
_tooltip.SetToolTip(portNumber, "Tooltip for portnumber");
_tooltip.SetToolTip(portNumber.Controls[0], "Tooltip for portnumber");
_tooltip.SetToolTip(portNumber.Controls[1], "Tooltip for portnumber");
This way the hover works normally as expected anywhere in the control.