  We demonstrate control of the differential Zeeman shift between clock states
of ultracold rubidium atoms by means of non-resonant microwave dressing. Using
the dc-field dependence of the microwave detuning, we suppress the first and
second order differential Zeeman shift in magnetically trapped $^{87}$Rb atoms.
By dressing the state pair 5S$_{1/2} F= 1, m_F = -1$ and $F= 2, m_F = 1$, a
residual frequency spread of <0.1 Hz in a range of 100 mG around a chosen
magnetic offset field can be achieved. This is one order of magnitude smaller
than the shift of the bare states at the magic field of the Breit-Rabi
parabola. We further identify double magic points, around which the clock
frequency is insensitive to fluctuations both in the magnetic field and the
dressing Rabi frequency. The technique is compatible with chip-based cold atom
systems and allows the creation of clock and qubit states with reduced
sensitivity to magnetic field noise.
