How to sanitize post meta field value?

HTML in custom fields is, from my point of view, a weird use case of custom fields. Even more if the purpose of the used HTML is just look and feel (<strong> and <i> can be seen as just look and feel). It is really better if you use the HTML markup on the custom field output or if you use CSS to apply bold/italic styles.

That being said, you can try to use PHP strip_tags() function or wp_kses() function. Both allow you to strip HTML tags but allow some of them. Example using wp_kses():

$allowed_html = array(
    'i' => array(),
    'strong' => array(),
);

if( isset( $_POST['my_field'] ) ){

    $meta_value = wp_kses( $_POST['my_field'], $allowed_html );

    update_post_meta( $post->ID, 'my_field', $meta_value );

}