I have a long-standing personal rule about sending hand-written thank you notes to any prospects that agree to meet with me. I recently expanded my thank you note rule to include the speakers of any business events I attend. When the event concludes I make my way to the speaker and introduce myself and engage in conversation. I will also ask for their business card before leaving. I generally send out my thank you cards within a week of meeting someone.
I believe it is simply good manners to thank someone. However, it also can help you if you intend on following up with that person to pursue a business partnership. Your thank you card may help you stand out in that person’s mind and thereby they’ll be inclined to meet you again.