How can a gentleman know when a young lady regards his flirtatious comments with genuine interest?

Some young ladies do appreciate the attention of an older gentleman. A conversation often begins casually between strangers. The window of opportunity to connect may be limited. It is hard to tell if she is teasing or actually taking the flirting to heart. I think that she may feel awkward and unwilling to show her true interest. I do not want to be too blunt for fear of embarrasment. What can I say or do, in a polite way, to get an honest response from her?