Ledesma fired an effort from all of 30 yards onto the crossbar in a poor game at the New York Stadium.
Rotherham almost took an early lead through a Forest mistake. Kelvin Wilson put a little bit too much onto a pass back to goalkeeper Karl Darlow, who made a mess of his kick, before eventually clearing away from the lurking Alex Revell.
Neither side had been good in possession and were restricted to shots from distance. Paul Green fired well over for the home side while – at the other end – Dexter Blackstock’s effort was blocked.
Michail Antonio twice tried to make his pace pay with differing results. He ran the first ball at Scott Wootton out of play but then beat him and put in a teasing cross that Blackstock could only nod wide past onrushing keeper Adam Collin.
Antonio then almost picked out Britt Assombalonga moments later with another cross from the left but the striker could not get enough on it to divert it goalwards.
The highlight of the game came when Ledesma’s effort rattled the crossbar before bouncing away to safety but Darlow had been beaten all ends up.
Encouraged, Rotherham carved out another opportunity down the left flank with Reece James finding fellow loan player Tom Lawrence in the box – but he side-footed his effort wide of goal.
Antonio continued to look threatening in the second period and put in a good cross for Henri Lansbury to power a header over the bar.
Lansbury then had to display his defensive attributes to block Ledesma’s effort from the edge of the penalty area.
Forest had a goal chalked off before the hour mark when Blackstock was deemed to have committed a foul before powering a header in.
Rotherham’s Ben Pringle then missed a glaring chance after good work from Lawrence. Pringle, on his weaker right foot, scooped over from six yards out.
Lawrence then showed good skill before curling an effort just over the top corner from outside of the box.
The home side had largely been on top and Ledesma again looked the most likely to open up the scoring but a powerful effort went harmlessly wide.
James was the next to try his luck with a driving effort but Darlow got enough on it to clear the ball to safety.
Forest did have their opportunities to nick the win. Eric Lichaj volleyed one over from distance and Assombalonga failed to get a touch on a cross from Jamie Paterson.
Tom Ince was brought on by Stuart Pearce and Jordan Bowery entered the fray for the Millers but a late winner never looked likely for either side.