Both B757 FMC's locked up during climb on an oceanic leg. After conferring with Maintenance the FMC circuit breakers were pulled and reset which returned both systems to normal operation.

Narrative

Enroute; approximately 15 minutes after takeoff; climbing through FL210; route dropped out of both CDU's; standby one annunciated on scratch pad of both CDU's. Have seen this before and usually just takes about 90 seconds or so for the computers to resync. After a few minutes with nothing happening; started the clock to keep track of time that units were off line. CDU's were locked up and would not accept any input. I had First Officer contact Dispatch and Maintenance via VHF radio. Once they were on I transferred control of aircraft to First Officer and talked to Maintenance and Dispatch. Maintenance mentioned as per Maintenance Manual I could cycle circuit breakers on left and right CDU; but that it could only be accomplished under Emergency Captain's Authority. I told them I would utilize that authority and cycle the CB's. Captain's CDU went out and then came back online. [It] did the same to the First Officer's. Upon cycling the right side CDU's unfroze and we were able to enter the waypoints for our route. Confirmed out position with ATC and proceeded on course to our destination. [We] notified Maintenance and Dispatch that everything appeared normal and would be proceeding to our destination. Flight proceeded normal after that.