  We present a detailed characterization of coherence in seven transmon qubits
in a circuit QED architecture. We find that spontaneous emission rates are
strongly influenced by far off-resonant modes of the cavity and can be
understood within a semiclassical circuit model. A careful analysis of the
spontaneous qubit decay into a microwave transmission-line cavity can
accurately predict the qubit lifetimes over two orders of magnitude in time and
more than an octave in frequency. Coherence times $T_1$ and $T_2^*$ of more
than a microsecond are reproducibly demonstrated.
