Objective: Surface electromyography (sEMG) is a noninvasive option for monitoring respiratory effort in ventilated patients. However, respiratory sEMG signals are affected by crosstalk and cardiac activity. This work addresses the blind source separation (BSS) of inspiratory and expiratory electrical activity in single- or two-channel recordings. The main contribution of the presented methodology is its applicability to the addressed muscles and the number of available channels. Approach: We propose a two-step procedure consisting of a single-channel cardiac artifact removal algorithm, followed by a single- or multi-channel BSS stage. First, cardiac components are removed in the wavelet domain. Subsequently, a nonnegative matrix factorization (NMF) algorithm is applied to the envelopes of the resulting wavelet bands. The NMF is initialized based on simultaneous standard pneumatic measurements of the ventilated patient. Main results: The proposed estimation scheme is applied to twelve clinical datasets and simulated sEMG signals of the respiratory system. The results on the clinical datasets are validated based on expert annotations using invasive pneumatic measurements. In the simulation, three measures evaluate the separation success: The distortion and the correlation to the known ground truth and the inspiratory-to-expiratory signal power ratio. We find an improvement across all SNRs, recruitment patterns, and channel configurations. Moreover, our results indicate that the initialization strategy replaces the manual matching of sources after the BSS. Significance: The proposed separation algorithm facilitates the interpretation of respiratory sEMG signals. In crosstalk affected measurements, the developed method may help clinicians distinguish between inspiratory effort and other muscle activities using only noninvasive measurements.