The performance of a quantum processor depends on the characteristics of the device and the quality of the control pulses. Characterizing cloud-based quantum computers and calibrating the pulses that control them is necessary for high-fidelity operations. However, this time-intensive task eats into the availability of the device. Here, we show restless measurements with a dynamic repetition rate that speed-up calibration and characterization tasks. Randomized benchmarking is performed 5.3 times faster on the quantum device than when an active reset is used and without discarding any data. In addition, we calibrate a qubit with parameter scans and error-amplifying gate sequences and show speed-ups of up to a factor of 40 on the quantum device over active reset. Finally, we present a methodology to perform restless quantum process tomography that mitigates restless state preparation errors. These results reduce the footprint of characterization and calibration tasks. Quantum computers can thus either spend more time running applications or run calibrations more often to maintain gate fidelity.