Spatial capture -recapture (SCR) is a popular and robust method for estimating population density, abundance, and dynamics. In systems where leaving stationary detectors in the field is not practical, data for SCR analyses is often collected with moving detectors (e.g., photo identification surveys from a boat, scat detection dogs). In these cases, the path of the moving detector is typically discretized and converted, post hoc, into a grid of ‘effective’ traps. While in most cases this approach is effective, we demonstrate that for some datasets this results in biased density estimates. We developed a new SCR method specifically for this data type with a likelihood formulated for detectors that move in space and time. We present a simulation study that highlights the reduction in bias, improvement in precision, and reduction in computation time afforded by our new method in specific cases and offer recommendations for when this approach is appropriate. We also demonstrate the improvements to inference with a case study of a population of Tamanend’s bottlenose dolphin (Tursiops erebennus) in the southeastern US. This method, which is available in the openpopscr package on Github, has wide applicability to species sampled via search-encounter surveys in terrestrial and marine systems.