It really depends what you're doing, and how important the colour-accuracy is.
If it's just "so they look the same", you can probably do it by eye. Bring up a photo on both montiors (Macie the KODAK Digital LAD Test Image is good for this), then fiddle with the settings until they look the same. Typically you reset everything on both monitors (which can often get you most of the way there), then adjust the contrast, then brightness then colour-balance till the two match.
I also found "Monitor Color Calibration for free using your DSLR", which describes using a DSLR to calibrate a monitor. It's not exactly a one-click-and-everything-is-perfect setup, but it seems to work..
The Datacolor Spyder series seem to be about the most popular monitor calibration probe, and are quite reasonably priced (about $150USD according to froogle.com)
At the last place I worked, they used (well, originally developed!) cineSpace for monitor-profiling/calibration - although it's not exactly cheap, from here, "Pricing for cineSpace starts at 1,000.00 USD for a basic cineSpace license package". cineSpace is likely overkill for what you are doing, although you do mention your machine having a nVidia Quadro card which implies some form of high-end visual "stuff"..
In short, try doing it by eye (or using a DSLR). If that doesn't work, look into the Spyder 3.
On Windows 10, with Intel graphics:
Method 1:
Right click on the desktop and select 'Display Settings' (or get here from any of the other many ways possible).
Click on 'Advanced display settings' at the bottom.
Click on 'Display adapter properties' at the bottom of the screen.
Click on the 'Intel (r) HD Graphics Control Panel' tab.
Select the display for which you need to change the rotation.
On the 'Rotation' setting, click on the desired rotation option and click ok.
Method 2: (which I just found right after I used Method 1)
Right click on the desktop and select the 'Graphics Options' menu.
Select the 'Rotation' sub menu.
Select the display for which you need rotation to be set in the next sub menu.
Select the rotation option from the final sub menu.
Method 3:
CTRL+ALT+[Arrow Key] works in this scenario as well. Note that this rotates the monitor on which the mouse pointer is on.
Best Answer
That shortcut is typically enabled through the Nvidia control panel. I have no idea if it is also available on ATI cards.
Take a look in the ATI / Nvidia program and see if you can enable it as a option, if it does not support the hotkeys, you should manually be able to rotate the screen.