Reliable on-chip power delivery is a challenging design task for sub-100nm and below VLSI technologies as voltage IR drops become more and more pronounced. This situation gets worse as technology continues to scale down. And efficient verification of power integrity becomes critical for design closure. In addition, the increasing process-induced variability makes it even worse for reliable power delivery networks. The process induced variations manifest themselves at different levels (wafer level, die-level and within a die) and they are caused by different sources (lithograph, materials, aging, etc.). In this dissertation, for power delivery networks without considering process variations, we propose an efficient simulation approach, called ETBR (Extended Truncated Balanced Realization), which uses MOR (Model Order Reduction) to speedup the simulation. To make ETBR more accuracy, we further introduce an error control mechanism into it. For power delivery networks with considering process variations, we propose varETBR (variational Extended Truncated Balanced Realization), a reduced Monte-Carlo simulation approach, which can handle a large number of variables and different variation distributions. To further speedup the MOR process used in the fast simulation, a hierarchical Krylov subspace projection based MOR approach, hiePrimor, is proposed. Besides the on-chip power delivery, excessive on-chip temperature has also become a first-tier design constraint as CMOS technology scales into the nanometer region. The exponential increase of power density of the high-performance microprocessors leads to the rapid rising of the average chip temperature. Higher temperature has significant adverse impacts on chip package cost, performance, and reliability. Multi-core techniques provide a viable solution to temperature/power problems. However, designing thermal efficient multi-core microprocessors remains a challenging problem as the temperature in each core can be dramatically different and the resulting large temperature gradients can produce mechanical stress and degrade the chip reliability. In this dissertation, we investigate a new architecture-level dynamic thermal characterization problem from a behavioral modeling perspective to address the emerging thermal related analysis and optimization problems for high-performance multi-core microprocessor design. We propose a new approach, called ThermPOF, to build the thermal behavioral models from the measured or simulated thermal and power information at the architecture level. And then we extend ThermPOF into ParThermPOF, a parameterized thermal behavioral modeling approach that can handle different parameters in multi-core microprocessor design and optimization.