The electromagnetic environment in which a small tunnel junction circu
it is embedded plays a crucial role in its transport properties. Altho
ugh the theory of single-electron tunneling is well established, few a
nalytical results are known. We use a real-time formulation to obtain
new predictions for the high-temperature conductance of single-and dou
ble-junction systems in series with a resistor. We discuss the implica
tions of our results for recently proposed metrological thermometry ba
sed on Coulomb blockade of single-electron tunneling.