Using Statamic HTML Caching with a dynamic Raven form. Put the form on a separate page and pull it in via JS.

form.html

<!--
  A template for raven stuff.
  
  Display this at a URL like /contact-form for example
  Exclude this URL from html_caching
  
  Make this form look/act like it was part of the parent page.
  The contents of #raven will be injected into it.
-->

<div id="raven">

  {{ if {raven:success} }}
	  ...
  {{ /if }}

  {{ if {raven:has_errors} }}
    ...
  {{ /if  }}

  {{ raven:form }}
    ...
  {{ /raven:form }}
  
</div>

form.js

// When the DOM is ready
$(function(){
  
  // Cache the element
  var formDiv = $('#contact-form');
  
  // Set the URL the form lives on
  var ravenURL = '/contact-form';
  
  // Perform an ajax request to the form page
  var req = $.ajax({
    url: ravenURL
  });
  
  // When the request is done...
  req.done(function(data){
    // Get the contents of the #raven div
    var ravenHtml = $(data).find('#raven').html();
    // and put it inside the #contact-form div 
    formDiv.html(ravenHtml);
  });
  
  // Hijack the form submission
  formDiv.on('submit', 'form', function(e){
    var form = $(this);
    // Don't submit the form
    e.preventDefault();
    // Submit it via ajax instead
    var req = $.ajax({
      url: ravenURL,
      data: form.serialize()
    });
    // When the request is done...
    req.done(function(data){
      // Get the contents of the #raven div
      var ravenHtml = $(data).find('#raven').html();
      // and put it inside the #contact-form div 
      formDiv.html(ravenHtml);
    });
  });
  
});

html_caching.yaml

enable: true
exclude: contact-form

parent.html

<!--
  The template where you want the form to be injected to.
  For example, a contact page.
  
  You *should* cache this page.
  
  The form will be injected into the #contact-form div with
  JavaScript, but without JS there will be a link to the
  form template anyway.
-->

<h1>Contact</h1>

<div id="contact-form">
  <a href="/contact-form">Send us a message using our form.</a>
</div>

<!-- Scripts should be placed in the appropriate place. -->
<script src="jquery.js"></script>
<script src="form.js"></script>

Changing the ajax call to

var req = $.ajax({
      url: ravenURL,
      data: form.serialize(),
      type: 'POST'
});

Seems to do the trick.