In this study, we enhance the dynamic connectedness measures originally introduced by Diebold and Yılmaz (2012, 2014) with a time-varying parameter vector autoregressive model (TVP-VAR) which predicates upon a time-varying variance-covariance structure. This framework allows to capture possible changes in the underlying structure of the data in a more flexible and robust manner. Specifically, there is neither a need to arbitrarily set the rolling-window size nor a loss of observations in the calculation of the dynamic measures of connectedness, as no rolling-window analysis is involved. Given that the proposed framework rests on multivariate Kalman filters, it is less sensitive to outliers. Furthermore, we emphasise the merits of this approach by conducting Monte Carlo simulations. We put our framework into practice by investigating dynamic connectedness measures of the four most traded foreign exchange rates, comparing the TVP-VAR results to those obtained from three different rolling-window settings. Finally, we propose uncertainty measures for both TVP-VAR-based and rolling-window VAR-based dynamic connectedness measures.