Contacts Directory Gadget
This would be an adaptation of the Membership Directory gadget to allow contacts to be listed. Additionally contacts would have access to a set of Privacy settings in their User Profile comparable to what members have today. A stronger user agreement or terms of service agreement might be required along with legal opt-in requirements and notifications for any contact using the system. A personal message sent by a member to a contact could be set to go through admins for approval, to use the organization's administrative email address, to allow the member to disclose his email address if he wishes, or to point the contact to send a personal message to the member from location on a public membership directory.
Wild Apricot currently has a Membership Directory gadget that uses a pretty secure personal messaging system: the sender of the message must provide his email address to the recipient but only if the recipient responds does the recipient disclose her/his/their email address. A degree of privacy is preserved. Aside from standard email and Wild Apricot email blasts the personal messaging system is the primary means of initiating contact inside our organization. We make very little use of our forums and will not reconsider using them more until the Listserv project is online (empty forums do not look good; email is what will make them show activity).
As a hobby group our organization has eclectic interests. Allowing a member to contact someone who has stated similar interests would allow us to better self-organize and to recruit potential members.