In this work, we report a dual-mode ferroelectrically programmable on-chip antenna. The antenna is built on a silicon wafer using complementary metal-oxide semiconductor (CMOS) processes and exhibits two programmable resonant modes: one in the super high frequency (SHF) range and one in the extremely high frequency (EHF) range. The SHF mode resonates at 8.5 GHz and exhibits ultrawideband (UWB) behavior, while the EHF mode resonates at 36.6 GHz. Both resonance frequencies can be tuned in a non-volatile fashion by controlling the ferroelectric polarization state of a Hafnium Zirconium Oxide (HZO) varactor monolithically integrated into the feed line. This programmability arises from the ferroelectric switching of the embedded HZO film, which results in a non-volatile variation of its permittivity upon application of a voltage pulse. Ferroelectric switching occurs at approximately ±3 V and induces maximum resonance frequency shifts of 381 MHz for the SHF mode and 3 GHz for the EHF mode, corresponding to fractional frequency changes of 4.5% and 8.3%, respectively. Unlike previously reported ferroelectrically tunable antennas, our reported antenna combines full integration, CMOS compatibility, higher operating frequency, compact footprint, and non-volatile programmability.