A BOEING VC-137B-BW, USAF #58-6971, OPERATING AS AIR FORCE 2 (AF-2), DEPARTED CLEVELAND, OH, AT ABOUT 1745 EDT ON AN IFR CLEARANCE. AFTER DEPARTING CLEVELAND, AF-2 WAS ASSIGNED AN ALT OF 8000 FT MSL BY CLEVELAND DEPARTURE CONTROL & WAS TRANSFERED TO CLEVELAND ARTCC. ON INITIAL CONTACT WITH CLEVELAND ARTCC, AF-2 WAS CLEARED TO CLIMB TO FLT LEVEL 230. A CESSNA 310J, N3057L, WAS CRUISING IN THE SAME VICINITY ON AN IFR CLEARANCE AT 13,000 FT & WAS ALSO UNDER CONTROL OF CLEVELAND ARTCC. AS AF-2 WAS CLIMBING THRU 12,200, ARTCC'S ATC COMPUTER CONFLICT ALERT FUNCTION WAS ACTIVATED FOR BOTH ACFT, ALERTING THE CONTROLLER OF A PENDING LOSS OF REQUIRED SEPARATION. THE CONTROLLER INSTRUCTED AF-2 TO MAINTAIN 12,000 FT. AF-2 ACKNOWLEDGED. HOWEVER, AF-2 REACHED APRX 13,000 FT BEFORE STARTING DESCENT & SEPN CONTDDECREASING. RADAR DATA SHOWED A MIN SLANT RANGE DIST OF 1/4 MI WITH 600 FT VERT SEPN. THIS CONSTITUTED AN ATC OPERATIONAL ERROR INVOLVING LESS THAN STANDARD SEPN. THE ACFT WERE IN IMC & NONE OF THE PLTS SAW THE CONFLICTING TRAFFIC