Hello,

      Well i think the exception is because you are assigning the Reverse_Relationship_Name__c=firstRelType.Id without inserting the firstRelType. So you have to first off all insert thet value. Similarly you have used  firstRelType.Reverse_Relationship_Name__c  =  secondRelType.Id without inserting the secondRelType. So you have to insert that value first. Your code should be like this:

static testMethod void TestOrphanedRelDelete()

 {     

     Contact firstContact = new Contact (      FirstName='Joe',      LastName='Johanssen'    );   

     insert firstContact;
    Contact secondContact = new Contact (      FirstName='Bobby',      LastName='Johanssen'    );   

     insert secondContact;
     Relationship_Type__c firstRelType = new Relationship_Type__c (      Name='&&Test_Relationship 1'    );       

     insert firstRelType;

     Relationship_Type__c secondRelType = new Relationship_Type__c (      Name='&&Test_Relationship 2',                            

     Reverse_Relationship_Name__c = firstRelType.Id    );           

     insert secondRelType;

     firstRelType.Reverse_Relationship_Name__c = secondRelType.Id;   

     update firstRelType;    
    Relationship__c[] crel = new Relationship__c[]

    {      new Relationship__c(contact__c = firstContact.id, Relatedcontact__c = secondContact.id,        

           Relationship_Type__c=firstRelType.Id)   

    };   

   insert crel;        // check that rel gets created   

   Relationship__c crel_original = [select id,   Description__c,Relationship_Type__c,reciprocalrelationship__c from    

   Relationship__c where id=:crel[0].Id];    //relationship should be set right        System.assertEquals(crel_original.Relationship_Type__c, firstRelType.Id);
    // check for mirror rel    Relationship__c crel_mirror = [select id, Description__c, reciprocalrelationship__c, Relationship_Type__c from Relationship__c where reciprocalrelationship__c=:crel_original.Id];    //mirror should reference the original    System.assertEquals(crel_mirror.reciprocalrelationship__c, crel_original.Id);    Contact secondContactForDelete = [select id from contact where id=:secondContact.id];    Test.startTest();    delete secondContactForDelete;    Test.stopTest();    // test change to the rel    Relationship__c[] orphanedCrel = [select id from Relationship__c where id = :crel_original.Id];    //original should have updated relationship    System.assertEquals(0, orphanedCrel.size());  }}

Think this will resolve four exception.