Blind questions like this one are troublesome, because we are forced to assume important details that could mislead our advice.
Here's a safe answer: A 14-gauge steel plate would make a very rigid backing material. Or if it is reeeeally big, aluminum would weigh less.
Size and environmental conditions are important. Moisture, heat, and variable conditions could contribute to warping if it happens after-the-fact.
Or is this a mounting problem? Maybe all you need are suggestions on mounting that would defeat warping of the materials you already use.
What is being framed? If it is paper art, the answer might be completely different than if it is a matched set of 6 hunting rifles.
How much preservation do you need? If it is a poster, Gatorboard is OK. If it is a $10,000 giclee, be very careful to avoid that piece of advice. If it is 3-dimensional, lots of things could cause warping.
Your warping problem is probably not caused by the board itself, so choosing another board might not help at all.
Care to elaborate?