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// CATEGORY
$cat = Mage::getResourceModel('catalog/category_collection')->addFieldToFilter('name', 'Category_Name_Here');
$cat->getFirstItem()->getEntityId();

// SUBCATEGORY
$category = Mage::getResourceModel('catalog/category_collection')
    ->addFieldToFilter('name', 'Men')
    ->getFirstItem() // The parent category
        ->getChildrenCategories()
        ->addFieldToFilter('name', 'Clothing')
        ->getFirstItem(); // The child category

$categoryId = $category->getId();