Add a new input field, label it "Please leave blank", hide it using CSS, and ignore the post if that field is filled in. Something like this:
<style type='text/css'>
#other_email_label, #other_email {
display: none;
}
</style>
...
<form action='mail'>
<label id='other_email_label' for='other_email'>Please leave blank:</label>
<input type='text' name='other_email' id='other_email'>
...
</form>
So a human being won't see that field (unless they have CSS turned off, in which case they'll see the label and leave it blank) but a spam robot will fill it in. Any post with that field populated must be from a spam robot.