x264 can calculate both, PSNR and SSIM, by using "--psnr" and/or "--ssim". If you use those, you should also set "--preset psnr" or "--preset ssim", respectively.
As for other H.264 encoders, I don't know if they have a similar feature, but you may always use the MSU tool:
http://compression.ru/video/quality_...t_tool_en.html
Having said that, you should be aware that objective quality metrics, such as PSNR or SSIM are
not very good to judge the overall quality
(We all know that the "Psy" optimizations in x264 can give a great
perceived quality improvement, still they significantly
hurt the PSNR and SSIM metrics)