Trying to run a procedure, error says result consist more than one line
I don't understand why does you want to implement this in the SP form, but if, then (a variant with minimal edition)

DELIMITER |;

CREATE PROCEDURE setRelocationFee(IN empID INT(20), OUT Rfee INT(20)) 
BEGIN
    DECLARE relocation varchar(50) default 0;
    SELECT city INTO relocation 
    FROM employees 
    LEFT JOIN offices ON employeeNumber = empID;

    SET Rfee = CASE relocation
               WHEN 'San Francisco' THEN '$10000'
               WHEN 'Boston'        THEN '$8000'
               WHEN 'London'        THEN '$20000'
               ELSE                      '$15000'
               END ;  
END |;

DELIMITER ;