TROPOMI (TROPOspheric Monitoring Instrument) measurements of tropospheric NO2 columns provide powerful information on emissions of air pollution by ships on open sea. This information is potentially useful for authorities to help determine the (non-)compliance of ships with increasingly stringent NOx emission regulations. We find that the information quality is improved further by recent upgrades in the TROPOMI cloud retrieval and an optimal data selection. We show that the superior spatial resolution of TROPOMI allows for the detection of several lanes of NO2 pollution ranging from the Aegean Sea near Greece to the Skagerrak in Scandinavia, which have not been detected with other satellite instruments before. Additionally, we demonstrate that under conditions of sun glint TROPOMI's vertical sensitivity to NO2 in the marine boundary layer increases by up to 60g %. The benefits of sun glint are most prominent under clear-sky situations when sea surface winds are low but slightly above zero (±2g mg s-1). Beyond spatial resolution and sun glint, we examine for the first time the impact of the recently improved cloud algorithm on the TROPOMI NO2 retrieval quality, both over sea and over land. We find that the new FRESCO+ (Fast Retrieval Scheme for Clouds from the Oxygen A band) wide algorithm leads to 50g hPa lower cloud pressures, correcting a known high bias, and produces 1-4×1015g molec.g cm-2 higher retrieved NO2 columns, thereby at least partially correcting for the previously reported low bias in the TROPOMI NO2 product. By training an artificial neural network on the four available periods with standard and FRESCO+g wide test retrievals, we develop a historic, consistent TROPOMI NO2 data set spanning the years 2019 and 2020. This improved data set shows stronger (35g %-75g %) and sharper (10g %-35g %) shipping NO2 signals compared to co-sampled measurements from OMI. We apply our improved data set to investigate the impact of the COVID-19 pandemic on ship NO2 pollution over European seas and find indications that NOx emissions from ships reduced by 10g %-20g % during the beginning of the COVID-19 pandemic in 2020. The reductions in ship NO2 pollution start in March-April 2020, in line with changes in shipping activity inferred from automatic identification system (AIS) data on ship location, speed, and engine.