High-temperature superconducting YBa2Cu3O7-d (YBCO) thin-film detectors with improved responsivities were developed for fast time-domain measurements in the THz frequency range. YBCO thin films of 30 nm thickness were patterned to micro- and nanobridges and embedded into planar log-spiral THz antennas. The YBCO thin-film detectors were characterized with continuous wave radiation at 0.65 THz. Responsivity values as high as 710 V/W were found for the YBCO nanobridges. Pulsed measurements in the THz frequency range were performed at the electron storage ring ANKA from the Karlsruhe Institute of Technology (KIT). Due to the high responsivities of the nanobridges no biasing was required for the detection of the coherent synchrotron radiation pulses achieving very good agreement between the measured pulse shapes and simulations.