Self-consistent quantum simulations are used to explore the high-frequency performance potential of carbon nantube field-effect transistors (CNTFETs). The cutoff frequency expected for a recently reported CNT Schottky-barrier FET is well below the performance limit, due to the large parasitic capacitance between electrodes. We show that using an array of parallel nanotubes as the transistor channel reduces parasitic capacitance per tube. Increasing tube density gives a large improvement of high-frequency performance when tubes are widely spaced and parasitic capacitance dominates but only a small improvement when the tube spacing is small and intrinsic gate capacitance dominates. Alternatively, using quasi-one-dimensional nanowires as source and drain contacts should significantly reduce parasitic capacitance and improve high-frequency performance. Ballistic CNTFETs should outperform ballistic Si MOSFETs in terms of the high-frequency performance limit because of their larger band-structure-limited velocity.