There are two other things to consider:
1) The airways maps have tables on them which give the controlling authority and contact frequency for every airway/UAR, divided sometimes between reporting points, so reference to that is another way to find out the frequency.
2) It is good practice to leave the previous frequency selected in the other side of the flip flop or on the other radio (if you have one). If you have problems with the new frequency you can go back to the old one to confirm you have the correct numbers or ask them to call the next centre or sector on the phone to see if they can hear you or get another frequency.
Using other aircraft to find it out is not really a good idea, as sometimes in vertically split sectors he might be on a different frequency to the one you need. It's a bit like not bothering with navigation; you just follow him!