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We consider the inspiral of black holes carrying U(1) charge that is not electromagnetic, but corresponds to some dark sector. In the weak-field, low-velocity regime, the components follow Keplerian orbits. We investigate how the orbital parameters evolve for dipole-dominated emission and find that the orbit quickly circularises, though not as efficiently as for a gravitationally dominated emission. We then regard circular orbits, and look for modifications in the gravitational waveform from the components carrying small charges. Taking this into account we populate the waveform with simplified LIGO noise and put it through a matched filtering procedure where the template bank only consists of uncharged templates, focusing on the charges' effect on the chirp mass estimation. We find a consistent overestimation of the `generalised' chirp mass, and a possible over- and underestimation of the actual chirp mass. Finally, we briefly consider the effect of such charges on hyperbolic encounters, finding again a bias arising from interpreting the generalised chirp mass as the actual chirp mass.