We explore the possibility to trap Rydberg atoms in tightly confining magnetic microtraps. The trapping frequencies for Rydberg atoms are expected to be influenced strongly by magnetic field gradients. We show that there are regimes where Rydberg atoms can be trapped. Moreover, we show that so-called magic trapping conditions can be found for certain states of rubidium, where both Rydberg atoms and ground state atoms have the same trapping frequencies. Magic trapping is highly beneficial for implementing quantum gate operations that require long operation times.