The biggest one I ever moved from Europe to YVR as carry on was 70x80 cm. I measured the clothing cabinet on the outbound flight and convinced the gate agent on return that it fits there. No issue on board in J cabin. The crew was happy to accommodate. The challenge and a major one was to clear it through security. The item was too big to go through the machine. Long story short, they carried it to customs area equipped with machines for screening regular luggage. The process took two hours and involved dozen of various people. Needless to say, I was on my most polite behaviour with everybody. The painting was of very substantial value and I was ready to cancel my flight if needed.
I moved three different paintings of lesser value but bigger size as a fragile cargo. They have been professionally prepped for travel in Europe. All three of them have sustained minor and not visible damage to the frames. Old frames don't travel well, specifically the corners can't withstand vibrations. In my situation, the corners have slightly dislodged (by fraction of the millimeter) despite professional caging. It has been later on all fixed at the gallery in Vancouver.
What is my entire point here? Even if your painting is of no special value, the old frame might very well be! Cage the painting and secure the corners the best you can! If it is only sentimental piece just bubble wrap and put inside a TV box. Check in as fragile and with some luck they will not even charge you extra (technically they can for everything over linear 158 cm.). If you try to clear the security ( 60 cm is too wide for the belt but should fit at 45 degrees angle if fed manually from both sides of the machine ) and board with it, you will be at the mercy of all the uniformed "dragons" Best of luck anyway and let us know!!!