If the above doesn't work, try this. Go to C:\Users\YourUserName\AppData\Local\SWTOR\swtor\settings\ and change the refresh rate in the client_settings.ini file to 60 or whatever your monitor can handle. Make sure hidden files/folders are visible and this location is for Windows 7/Vista so you may have to search if you're using an older version. Good luck!

If updated drivers doesn't fix the problem (it didn't for me), try this: Go to C:\Users\YourUserName\AppData\Local\SWTOR\swtor\settings and change the refresh rate in the client_settings.ini file to 60 or something your monitor can handle. Save and restart the game. That location is for Windows Vista / 7, so if you have an earlier version of Windows you may have to search. Also make sure you have hidden files/folders set to visible. Good luck!