At the moment there is a simple tool called Advanced Search for contacts, which gives you all of the fields that you have saved against contacts, from the standard First Name and Last Name to the Custom Fields that you have added also. However, there is no Advanced Search currently in the system for Organisation.
What you can do though, is run a report on your organisations using the Reporting Tool on the left hand menu and then selecting Business Reports. This will allow you to apply filters to your list of organisations and then come up with a list of Contacts attached to those organisations so you can communicate with them!