Nonce and widget

You have to be more clear about your problem. It will be better to publish you code and anyone can check it a give their help.

I have created a contact form before with nonce and inside the form i added:
<input type="hidden" name="nonce" value="<?php echo wp_create_nonce('send_email_nonce'); ?>"/>

and on the on the form handler i added:

$formNonce = $_POST['nonce'];

if (!wp_verify_nonce($formNonce, 'send_email_nonce')) {
  echo json_encode(array(
    'success' => false,
    'message' => __('Nonce was not verified!', 'shomtek')
  ));
  die;
}

But it depends on what is the purpose of your widget and form. I suggest you to be more specific and post your code.