Does caffeine and ritalin (methylphenidate) go well together?

No: You will only increase your chances to get tachycardia or other cardiac arrythmias.

Additive Effects: Ritalin (generic methylphenidate) and caffeine are both psychostimulants. Ritalin is indicated in the treatment of attention deficit disorder. Caffeine is often consumed to enhance mental clarity and to combat sleepiness. Both have similar side effects including potential for insomnia and heightened anxiety. Since it is difficult to accurately dose caffeine, using both is discouraged.