Here is one alternative:


   With validEmail (EmailAddress)
     As (
Select te.EmailAddress
   From #tblEmails       te
Except
Select tne.EmailAddress
   From #tblNoEmail     tne
         )
Select tc.ContactID
      , tc.Contact
      , te.EmailID
      , te.ContactID
      , te.EmailAddress
   From #tblContacts     tc
Inner Join #tblEmails  te On te.EmailID = tc.ContactID
Inner Join validEmail  ve On ve.EmailAddress = te.EmailAddress;


Test for performance, of course...

Another option would be to create the no email the table exactly the same as the email table.  Then, you can perform an easy insert from the email table into the no email table using all columns.


  With validEmail
    As (
Select te.EmailID
     , te.ContactID
     , te.EmailAddress
  From #tblEmails       te
Except
Select tne.EmailID
     , tne.ContactID
     , tne.EmailAddress
  From #tblNoEmail     tne
       )
Select tc.ContactID
     , tc.Contact
     , ve.EmailID
     , ve.ContactID
     , ve.EmailAddress
  From #tblContacts     tc
 Inner Join validEmail  ve On ve.ContactID = tc.ContactID;


To further simplify the changes you need to make - create a view to replace the email table using the second version above and replace #tblEmail with your view.