There is literally no good option other than testing on a range of target hardware.
Simply testing on slower hardware isn't enough. Older cards are often on different driver series, meaning that they support a lower version of Direct3D or OpenGL.
Cards of similar speeds but from different manufacturers will have different behavior. The behavior can differ because of loose specifications of semantics in the D3D or GL specs allowing vendors to do things differently, because of the vendor added some enabled-by-default extensions, or because of plain conformance bugs. For example, it's common to write GLSL code that works on an NVIDIA card but fails on Intel or AMD hardware because the GLSL code doesn't actually conform to the GLSL spec but which NVIDIA's drivers accept anyway.
Even aside from the hardware, there's various configurations to test. Users don't always install the latest drivers; the NVIDIA 34x drivers are different in key ways from the 30x legacy drivers. Users don't always have exact same version of the OS that you do, and software that works well in Windows 8 might perform poorly or not even run on Windows 7.
The only - only - reliable way to ensure that your game runs well on target machines is to actually test it on them.
If you can't test it yourself, you're going to have to rely on getting others to help test it for you with pre-alpha nightly builds or the like. Plenty of hip indie games do that stuff these days.
A poor man's option you might have available would be the discrete GPU in your CPU. Most recent processors from either Intel or AMD have an integrated GPU. It might take some shenanigans (rebooting, changing BIOS settings, and moving monitor cables) to use. Some of the newer systems make it easier and can do the swap in software (maybe only under a VM or the like). Beware that even then, you're only testing your integrated GPU and not all the others you might want to stay compatible with. Just because it runs on your desktop's Haswell Intel GPU doesn't mean it'll run on a customers's older A10 AMD APU or mobile Sandy Bridge Intel GPU.
Short version: you have to test on the target machines to get meaningful feedback on compatibility.