How to delete a service operation if this error is encountered: "Unable to delete. References found in runtime tables." ?

Run these three SQLs to see if you've any data for the service operation which you want to delete. 

SELECT * FROM PSAPMSGSUBCON WHERE IB_OPERATIONNAME = 'service operation'

SELECT * FROM PSIBLOGHDR WHERE IB_OPERATIONNAME = 'service operation'

SELECT * FROM PSAPMSGPUBHDR WHERE IB_OPERATIONNAME = 'service operation'

If you do, then delete the data and you will be able to successfully delete the service operation..