  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.
