This paper proposes a multichannel wavelet kernel network (MWKN) modeling technique with a two-stage training technique for high-dimensional inverse modeling of microwave filters. The real and imaginary parts of the transmission and reflection characteristics are used as the model inputs, while the geometric parameters of the filter are designated as the outputs. Since the electrical signal in microwave inverse modeling encompasses multiple frequency components and complex information arising from the subtle dimensional changes in the metal pattern, the wavelet transform is introduced by leveraging its powerful multi-scale and approximate detail features to form the discrete wavelet convolution layer in the proposed MWKN. To adapt to the learning of approximate detailed features at different scales, the learnable parameters of this layer and the weights of the backbone network are adjusted in stages through a two-stage training strategy based on particle swarm optimization (PSO), which jointly promotes the rapid convergence of the model. Three numerical examples demonstrate the effectiveness and robustness of the proposed MWKN model. Compared with the traditional design method using electromagnetic (EM) simulation, this approach significantly and substantially reduces the repeated calculation time and is capable of predicting the geometry that meets the design specifications within 0.42 s.