An on-chip resonator is designed and fabricated using a standard 0.13-μm SiGe technology for millimeter-wave applications. The designed resonator is based on a unique structure, which consists of two broadside-coupled meander lines with opposite orientation. The equivalent LC circuit of the resonator is given, while the impact of the structure on the resonance frequencies is investigated. Using this structure along with capacitors, a compact bandpass filter (BPF) is also designed and fabricated. The measured results show that the resonator can generate a resonance at 57 GHz with the attenuation better than 13.7 dB, while the BPF has a center frequency at 31 GHz and a insertion loss of 2.4 dB. The chip size of both the resonator and the BPF, excluding the pads, is only 0.024 mm² (0.09×0.27 mm²).