manual excerpt stripping HTML tags

Take a look at this StackOverflow thread. Basically the solution they use is:

<?php
/******************************************************************************
* @Author: Richard Chonak
* @Date:   August 6, 2013
* @Description: Ensures closure of HTML tags opened in an automatically generated excerpt.
* Also trims off any trailing incomplete HTML tag at the end of the excerpt.
* @Tested: Up to WordPress version 3.6
*
* @Author: Boutros AbiChedid
* @Date:   June 20, 2011
* @Websites: http://bacsoftwareconsulting.com/ ; http://blueoliveonline.com/
* @Description: Preserves HTML formating to the automatically generated Excerpt.
* Also Code modifies the default excerpt_length and excerpt_more filters.
* @Tested: Up to WordPress version 3.1.3
*******************************************************************************/
function custom_wp_trim_excerpt($text) {
$raw_excerpt = $text;
if ( '' == $text ) {
    //Retrieve the post content.
    $text = get_the_content('');

    //Delete all shortcode tags from the content.
    $text = strip_shortcodes( $text );

    $text = apply_filters('the_content', $text);
    $text = str_replace(']]>', ']]>', $text);

    $allowed_tags = '<img>,<small>,<strong>,<em>,<b>,<i>,<p>,<br>,<a>,<blockquote>,<ul>,<li>'; /*** MODIFY THIS. Add the allowed HTML tags separated by a comma.***/
    $twopart_tags = '<small>,<strong>,<em>,<b>,<i>,<p>,<br>,<a>,<blockquote>,<ul>,<li>'; /*** MODIFY THIS. Add the twopart HTML tags separated by a comma.***/
    /* turn tag list into one big search pattern */
    $search_patterns = "/" . str_replace(",","|",str_replace(">", "[^>]*>",$twopart_tags)) . '/';

    $text = strip_tags($text, $allowed_tags);

    $excerpt_word_count = 200; /*** MODIFY THIS. change the excerpt word count to any integer you like.***/
    $excerpt_length = apply_filters('excerpt_length', $excerpt_word_count); 

    $excerpt_end = '[...]'; /*** MODIFY THIS. change the excerpt endind to something else.***/
    $excerpt_more = apply_filters('excerpt_more', ' ' . $excerpt_end);

    $words = preg_split("/[\n\r\t ]+/", $text, $excerpt_length + 1, PREG_SPLIT_NO_EMPTY);
    if ( count($words) > $excerpt_length ) {
        array_pop($words);
        $text = implode(' ', $words);
        $text = $text . $excerpt_more;
    } else {
        $text = implode(' ', $words);
    };

    /* if fragment ends in open tag, trim off */
    preg_replace ("/<[^>]*$/", "", $text);

    /* search for tags in excerpt */
    preg_match_all ($search_patterns, $text, $matches);
    /* if any tags found, check for matching pairs */
    $tagstack = array ("");
    $tagsfound = $matches[0];
    while ( count ($tagsfound) > 0) {
        $tagmatch = array_shift($tagsfound);
    /* if it's a closing tag, hooray; but if it's not, then look for the closer */
        if ( !strpos($tagmatch,"</") && !strpos ($tagmatch,"/>") ) {
      preg_match("/\pL+/",$tagmatch, $tagwords);
          $endtag = "</" . $tagwords[0] . ">";
          /* if this tag was not closed, put the closing tag on the stack */
          if (!in_array($endtag, $tagsfound) ) {
        array_push($tagstack,$endtag);
          };
        };
    };

    /* if any unbalanced tags were found, add the closing tags */
    while (count ($tagstack) > 1) {
    $text = $text . array_pop($tagstack);
    }
}
return apply_filters('wp_trim_excerpt', $text, $raw_excerpt);
}
remove_filter('get_the_excerpt', 'wp_trim_excerpt');
add_filter('get_the_excerpt', 'custom_wp_trim_excerpt');
?>

Sorry for the length…