Matrix offers every user the option to create a "frameable" IDX search for use on their website.  This is a basic listing search, but it does offer a "Sign up form" option.  If you are using the Matrix IDX option, and have chosen to add the sign up form to the search, a person on your website can use this form to send you a contact request.  This is a simple form that allows them to send their name, email address, phone number, and a short message to you through the MLS.  People who have done this will show up in the "Contact Requests" widget.  Click on any name you see here, and Matrix will open a window to allow you to save them into your contact list:

From here, you can "Add" to save them to your Matrix Contact's list, "Delete" to deny the request, or "Cancel" to leave it in the "Contact Requests" widget for later review.