Seismic signals generated by iceberg calving can be used to monitor ice loss at tidewater glaciers with high temporal resolution and independent of visibility. We combine the Empirical Matched Field (EMF) method and machine learning using Convolutional Neural Networks (CNNs) for calving event detection at the SPITS seismic array and the single broadband station KBS on the Arctic Archipelago of Svalbard. EMF detection with seismic arrays seeks to identify all signals generated by events in a confined target region similar to single P and/or S phase templates by assessing the beam power obtained using empirical phase delays between the array stations. The false detection rate depends on threshold settings and therefore needs appropriate tuning or, alternatively, post-processing. We combine the EMF detector at the SPITS array, as well as an STA/LTA detector at the KBS station, with a post-detection classification step using CNNs. The CNN classifier uses waveforms of the three-component record at KBS as input. We apply the methodology to detect and classify calving events at tidewater glaciers close to the KBS station in the Kongsfjord region in Northwestern Svalbard. In a previous study, a simpler method was implemented to find these calving events in KBS data, and we use it as the baseline in our attempt to improve the detection and classification performance. The CNN classifier is trained using classes of confirmed calving signals from four different glaciers in the Kongsfjord region, seismic noise examples, and regional tectonic seismic events. Subsequently, we process continuous data of 6 months in 2016. We test different CNN architectures and data augmentations to deal with the limited training data set available. Targeting Kronebreen, one of the most active glaciers in the Kongsfjord region, we show that the best performing models significantly improve the baseline classifier. This result is achieved for both the STA/LTA detection at KBS followed by CNN classification, as well as EMF detection at SPITS combined with a CNN classifier at KBS, despite of SPITS being located at 100 km distance from the target glacier in contrast to KBS at 15 km distance. Our results will further increase confidence in estimates of ice loss at Kronebreen derived from seismic observations which in turn can help to better understand the impact of climate change in Svalbard.