In November 2014, a temporary land and marine seismic network was deployed to monitor the drilling of an exploratory well in the Canary Channel (eastern Canary Islands). This region is characterized by low‐seismic activity; however, because of the increased awareness of the potential seismic hazard caused by hydrocarbon exploitation activities, the drilling operations were monitored with an unprecedented level of detail for an activity of this kind. According to the reported earthquakes, there was not a measurable increase in seismicity in the vicinity of the well. Overall seismic activity was low, which is consistent with the historical seismicity records. Harmonic tremor, explained here as resonances of the instrument‐seafloor system generated by bottom water currents in the area, was commonly detected on the ocean‐bottom seismometer (OBS) recordings. The marine network data also revealed dozens of nonseismic short‐duration signals per day that appear similar to other events on OBS recordings throughout the world. We suggest that they may be caused by direct perturbations on the OBS, mostly induced by ocean currents in the Canary Channel.