You could load the options collection and filter by product id and title.
$options = Mage::getModel('catalog/product_option')
->getCollection()
->addTitleToResult(Mage::app()->getStore()->getId())
->addPriceToResult(Mage::app()->getStore()->getId())
->addProductToFilter(array('product_id'))
->addValuesToResult()
->addFieldToFilter('default_option_title.title', 'Option title');
With the title there is a default option and also a store title so you should us either of the following lines.
->addFieldToFilter('default_option_title.title', 'Option title')
->addFieldToFilter('store_option_title.title', 'Option title')