We have used x-ray magnetic circular dichroism (XMCD) and ab initio electronic-structure calculation techniques to investigate the magnetic properties of high-quality epitaxial (110) and (100) CrO2 thin films. A relatively larger XMCD was observed on the Cr L2,3 edge of (110)-oriented CrO2 films compared to (100)-oriented CrO2 films at room temperature. Analysis of our data with conventional sum rules for 3d elements shows a nearly 50% higher spin moment on (110) films compared to (100) orientation, consistent with bulk magnetometry measurements. The orbital moment is found to be similar for both orientations. Robust magnetism is attributed to increased collinearity of Cr spins in strain-free (110) films as compared to strained (100) films. Zero-temperature density-functional calculations show opposing trends in nearest-neighbor and next-nearest-neighbor exchange interactions between relaxed and strained CrO2.