Hana uses Apple's Webkit technology to bring the best web and javascript rendering to Hana. This includes Webkit's security.
Hana includes a setting to be alerted when the page you are currently viewing switches from using a secured connection to a non-secured connection and vice-versa.
Hana 1.1 now features the inclusion of a small padlock icon on the tab of any web-app that is being secured via SSL. This way you know when your web-app is connected to its host securely.