The 2.0 API provides support for `/search`:

<pre>http://api.stackexchange.com/2.1/search?site=<b>[site]</b>&intitle=<b>[search string]</b></pre>

If you want to constrain this to your posts, 2.0's `/search/advanced` path allows you to filter by user, [or by basically anything else](https://api.stackexchange.com/docs/advanced-search):

<pre>http://api.stackexchange.com/2.1/search/advanced?site=<b>[site]</b>&title=<b>[search string]</b>&user=<b>[your user ID]</b></pre>

Beware - `/search` calls the title parameter `intitle`, while `/search/advanced` calls it `title`.