This work introduces high-speed (390 Hz) speckle contrast optical spectroscopy (SCOS) to enable simultaneous measurements of multi-anatomic site microvascular blood volume and flow oscillations. Simultaneous blood flow and volume waveforms were extracted at two wavelengths on the wrist and finger, in reflectance and transmission mode, respectively. Blood volume changes (also known as photoplethysmography, or PPG) were determined based on intensity oscillations. Blood flow information was determined based on dynamic light scattering information encoded in the 2D spatial speckle pattern after removal of stochastic and instrument noise. We extracted a wide array of temporal, shape-based, and frequency-domain features from each high-resolution waveform, as well as features that characterize the temporal relationships between these features. These features and their inter-relationships are determined by the dynamic biomechanical properties of peripheral microvasculature, including vascular compliance and resistance, which are key determinants of dynamic changes in systemic blood pressure (BP). In comparison to PPG alone, SCOS demonstrated a notable 31% improvement (p = 3.45 * 10) in systolic BP estimation when integrated into subject-specific machine-learning models. The resulting errors were remarkably low (systolic BP: 0.06+/- 2.88 mmHg, diastolic BP: 0.09 +/-2.14 mmHg) across a wide range of BP variations (range SBP: 89-284 mmHg). This improvement was sustained several weeks later within a re-measured cohort, indicating highly robust BP predictions. Looking ahead, high-speed SCOS holds the potential to substantially enhance the non-invasive characterization of the cardiovascular system, including continuous and non-invasive BP measurements, which are a long-sought-after goal of the biomedical community.