If you can get the a graphic format of the subtitles (ifo/sup, idx/sub, etc.), you can upscale them with BDSup2Sub to HD sizes.
The program allows you to resize with various filter methods (from bilinear & bicubic to Lanczos3 & Mitchell), retime, change frame rates (good if you're using a PAL source) and more.
Output formats include BD SUP. This way you don't have to mess with OCR.