In the United States, food products labeled as “organic” are generally believed to be in compliance with the standards of the National Organic Program (NOP), a program of the USDA, which strictly prohibits the use of GMO's under that certification, but even in countries that require GMO labeling, the standard legal threshold of 0.9% is the potential percentage of GMO content that could be present. For this reason, the FDA discourages the use of the term “GMO Free” since all food items may contain trace amounts of GMO's. Farms and processors with $5,000 or less in gross income from organic sales are exempt and may label products as organic without any certification, even if they contain GMO's. Some producers will even bust up their operation into smaller outfits to slip through this loophole, but more often they will simply violate the restrictions undetected. I only mentioned the above to illustrate some of the problems with certification.
It's important to note that USDA organic rules do not say a single word about sustainability, which remains a loosely defined term in most contexts these days. Sustainable, in the context of the growers I work with, means that the nutrients removed from the soil by growing plants are replenished without any artificial inputs. Even natural inputs must be sourced locally to adhere to this standard. We haven't discussed GMO crops, and I think it's because we never considered planting them.
In light of all this, many local groups opt to form their own consortium to develop standards that are important to them, such as agricultural sustainability as reflected in your question. Some of them do permit GMO's, but they show a strong preference for locally adapted heirloom varieties which outperform modified plants designed for mega-agriculture. Even if they could be proven perfectly safe for human consumption, I think the customers and the growers would still avoid them for other important and legitimate reasons.
Nothing stops you from growing GMO's sustainably using otherwise organic methods. You could form your own certification and certify others accordingly, but the main reason that this is not normally done is that the USDA certified "organic" standards are usually used as a baseline for other types of certification, which precludes the use of GMO's across the board.
If you had a class A setup with impressive sustainabile practices developing rich organic soil using no pesticides, herbicides, fungicides, or chemical fetilizers, something that I would certify as being "better than USDA organic," then I don't think you would even want to grow GMO crops. GMO crops seem to be a way to avoid addressing the more serious problems with agriculture.
On a larger scale, there are organizations such as The Green Business Bureau. With their certification process you receive points for each activity you complete. They help identify the sustainability efforts a business performs, while helping to outline future efforts. They are different from many other organizations because they make it easier for small businesses to develop and define their own sustainability practices.
For B-Corp certification, you get evaluated on how your company treats workers, customers, community, and environment. Sustainability is a major focus here. You have to get 80 points and maintain that level, but I don't think that freedom from GMO's is absolutely required before you get certified.
In addition, there are many awards available within specific growing regions that have identified concise goals required in order to be considered. With the award you get the right to display it. They are often much more careful about verifying adherence to organic practices and sustainability standards. Others seem to have no concern whatsoever about sustainability, or GMO's, or impact to the planet, and just award you for promoting the industry or growing the biggest pumpkin, but in some areas a certified safe GMO, if there were such a thing, would be banned anyway. In California, the counties of Marin and Mendocino have enacted ordinances forbidding the cultivation of GMOs, and in Hawaii's Kauai County and Hawaii County the cultivation of most GMO crops is banned.
In the end, a certification for GMO's would not make much sense because anyone who sees a "safe GMO" label is going to avoid it like the plague. How many producers are going to want to certify that their product actually contains GMO's when current US law allows them to hide it from the consumer? As is stands, you can brag about your sustainability on the label and include a note on how sustainable your GMO's are, but I imagine you would be shooting yourself in the foot there. Perhaps a certifying body would be formed if GMO labels were required either in the states or federally. Only then would producers want to certify their GMOs as safe and be willing to pay for that certification.
