© 2017 American Physical Society. We report on the performance of the capacitive gap-sensing system of the Gravitational Reference Sensor on board the LISA Pathfinder spacecraft. From in-flight measurements, the system has demonstrated a performance, down to 1 mHz, that is ranging between 0.7 and 1.8 aF Hz-1/2. That translates into a sensing noise of the test mass motion within 1.2 and 2.4 nm Hz-1/2 in displacement and within 83 and 170 nrad Hz-1/2 in rotation. This matches the performance goals for LISA Pathfinder, and it allows the successful implementation of the gravitational waves observatory LISA. A 1/f tail has been observed for frequencies below 1 mHz, the tail has been investigated in detail with dedicated in-flight measurements, and a model is presented in the paper. A projection of such noise to frequencies below 0.1 mHz shows that an improvement of performance at those frequencies is desirable for the next generation of gravitational reference sensors for space-borne gravitational waves observation.