The models for nanoelectronics coupled problems, such as electro-thermal (ET) coupled problems, are very large in scale. These models often include parameter variability to guarantee quality and yield. The parameter variations can be due to material properties, system configurations, etc. The scientific challenges are to develop efficient and robust techniques for fast simulation of strongly coupled systems that exploit the different dynamics of sub-systems, and that can deal with signals that differ strongly in the frequency range and parameter domain. However, direct application of the standard parameterized model order reduction (PMOR) techniques to the ET coupled models, may lead to inaccurate or unsolvable reduced-order models (ROMs) due to increased index and the mixing of field variables, and may not be able to capture the electro-thermal couplings. We propose a PMOR method for ET coupled models, which involves first decoupling the system into algebraic and differential parts, then applying the standard PMOR techniques to the decoupled parts, respectively.