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Modeling of waveguide junctions using transmission lines and lumped circuit elements is common practice in microwave networks. By the help of the scattering matrix formalism, it is possible to describe junction effects in a very concise way. Such a representation is crucial for the design of complex systems containing many interacting parts. Using scattering matrices, we characterize symmetric junctions between 2-D metal--insulator--metal (MIM) waveguides with optical signals at infrared frequencies (1550 nm) propagating in them. We verify our characterization by perfectly matching a wavelength-sized MIM waveguide to a subwavelength-sized one using a Smith chart. We then map the scattering matrix description to an equivalent lumped circuit representation and discuss the physical significance of its elements. We show that the simplified characteristic impedance model is appropriate for the deep subwavelength regime. The scattering matrix model for the MIM junctions leads to simplified analysis that can be integrated into circuit modeling software packages, such as SPICE.