How do I show multiple recaptchas on a single page?

With the current version of Recaptcha (reCAPTCHA API version 2.0), you can have multiple recaptchas on one page.

There is no need to clone the recaptcha nor try to workaround the problem. You just have to put multiple div elements for the recaptchas and render the recaptchas inside them explicitly.

This is easy with the google recaptcha api:
https://developers.google.com/recaptcha/docs/display#explicit_render

Here is the example html code:

<form>
    <h1>Form 1</h1>
    <div><input type="text" name="field1" placeholder="field1"></div>
    <div><input type="text" name="field2" placeholder="field2"></div>
    <div id="RecaptchaField1"></div>
    <div><input type="submit"></div>
</form>

<form>
    <h1>Form 2</h1>
    <div><input type="text" name="field3" placeholder="field3"></div>
    <div><input type="text" name="field4" placeholder="field4"></div>
    <div id="RecaptchaField2"></div>
    <div><input type="submit"></div>
</form>

In your javascript code, you have to define a callback function for recaptcha:

<script type="text/javascript">
    var CaptchaCallback = function() {
        grecaptcha.render('RecaptchaField1', {'sitekey' : '6Lc_your_site_key'});
        grecaptcha.render('RecaptchaField2', {'sitekey' : '6Lc_your_site_key'});
    };
</script>

After this, your recaptcha script url should look like this:

<script src="https://www.google.com/recaptcha/api.js?onload=CaptchaCallback&render=explicit" async defer></script>

Or instead of giving IDs to your recaptcha fields, you can give a class name and loop these elements with your class selector and call .render()