The meeting of tenth and 11th in the table produced no goals at a damp St Colman's Park.
The draw means that the home side are still unbeaten at home, but Pete Mahon's side will be happier with their second away draw in a week.
Ramblers went close to scoring in the first half and missed a penalty when Kieran O'Reilly's spot-kick was well saved by in-form UCD goalkeeper Matt Gregg.
The visitors went close when Derek Doyle sent a shot off the Cobh post and in the second half a Paul Byrne header brought a great save from Ramblers 'keeper James McCarthy.
Ramblers who had won their last home outing against Shamrock Rovers, their only win in the campaign so far, welcomed back captain and right-back Alan Carey.
John Kearney came in for Shane Barrett in midfield with Conor Meade taking over from Graham Cummins up front.
Pete Mahon's students had picked up a point, which might have been three, but for a stoppage time equaliser at Shamrock Rovers last week, and beat Bray on their travels on 14 March for their only league win of the season.
The home side opened brightly and created three chances in the first ten minutes, Conor Meade headed an Alan Carey cross wide of the target after 60 seconds from the edge of the six-yard box.
The UCD goalkeeper Matt Gregg was a busy man, first denying Davin O'Neill on the edge of the box, and then when it seemed he brought down Kieran O'Reilly, referee Neil Doyle booked the forward for diving.
But the Dublin official had no doubts on 27 minutes when he pointed to the spot after full-back Ian Bermingham appeared to foul Conor Meade in the penalty area.
But Gregg saved Kieran O'Reilly's weak spot kick on the goal line.
Just before that UCD might have scored but Derek Doyle's shot, which beat home goalkeeper James McCarthy, rebounded off a post and back into play.
Despite Cobh producing some very good football, the visitors, with wind advantage, again went close to the breakthrough when Alan Mahon set up Paul Byrne whose header brought a brilliant one-handed save from James McCarthy just after the hour.
In the end, Cobh remain unbeaten at St Colman’s Park after their four home league games, but it will be UCD who will be the happier with the point.
COBH: McCarthy; Carey, Guthrie, Murray, J Meade; O'Neill, A Kearney, J Kearney, Mulconry; C Meade, O'Reilly. Substitutes; Cambridge and Cummins for C Meade and O Neill both 72 mins, Coleman for J Kearney 83.
UCD: Gregg; Mahon, Bermingham, Kenna, Shortall, King, McWalter, Finn, Byrne, Doyle, Fitzgerald. Subs; Reilly for Doyle 80, Purcell for McWalter 90.
Referee: Neil Doyle(Dublin).
