Since this is about template customizing + for Zen-Cart v1.3x (and, correct, results are only found for older versions only) - sounds like fun. 
// Step 1:
In your includes/templates/<your_template>/tpl_contact_us_default.php file,
find:
PHP Code:
<label class="inputLabel" for="email-address"><?php echo ENTRY_EMAIL; ?></label>
<?php echo zen_draw_input_field('email', ($error ? $_POST['email'] : $email), ' size="40" id="email-address"') . '<span class="alert">' . ENTRY_REQUIRED_SYMBOL . '</span>'; ?>
<br class="clearBoth" />
add below:
PHP Code:
<label class="inputLabel" for="contactphonenumber"><?php echo ENTRY_TELEPHONE_NUMBER; ?></label>
<?php echo zen_draw_input_field('phone_number', $phone_number, ' size="40" id="phone_number"') . '<span class="alert">' . ENTRY_REQUIRED_SYMBOL . '</span>'; ?>
<br class="clearBoth" />
// Step 2:
In your includes/modules/pages/contact_us/<your_template>/header_php.php file,
find:
PHP Code:
$enquiry = zen_db_prepare_input(strip_tags($_POST['enquiry']));
add below:
PHP Code:
$phone_number = zen_db_prepare_input(stripslashes(trim($_POST['phone_number']))) : "";
Then, find:
PHP Code:
if ($zc_validate_email and !empty($enquiry) and !empty($name)) {
replace with:
PHP Code:
if ($zc_validate_email and !empty($enquiry) and !empty($name) and !empty($phone_number)) {
Then, find:
PHP Code:
$html_msg['EXTRA_INFO'] = $extra_info['HTML'];
add right below:
PHP Code:
$html_msg['PHONE_NUMBER'] = $phone_number;
Then, find:
PHP Code:
if (empty($enquiry)) {
$messageStack->add('contact', ENTRY_EMAIL_CONTENT_CHECK_ERROR);
}
add right below:
PHP Code:
if (empty($phone_number)) {
$messageStack->add('contact', ENTRY_EMAIL_PHONE_NUMBER_CHECK_ERROR);
}
// Step 3:
In your includes/languages/english/<your_language>/contact_us.php file,
add the following entries in:
PHP Code:
define ('ENTRY_TELEPHONE_NUMBER', 'Contact phone number:');
define('ENTRY_EMAIL_PHONE_NUMBER_CHECK_ERROR', 'You did not filled out your contact phone number.');
// Step 4:
In your email/email_template_contact_us.html file,
find:
add below:
Of course, the email template modifications part is only suggested - you can add this variable anywhere you'd like, from that template file, in order to fit your needs. 
I believe these should be all.