Utilizing 1-bit quantization at the analog-to-digital converter (ADC) is a promising approach to reduce the problematically high power consumption of high resolution ADCs in millimeter-wave (mmWave) and sub-terahertz (THz) communications. However, as 1-bit quantization is a highly nonlinear operation standard channel estimation algorithms cannot be applied. Therefore, we study algorithms for channel estimation in receivers with 1-bit quantization under consideration of a two-wave with diffuse power (TWDP) fading channel model, which was shown to be a realistic model for indoor communications in the mmWave regime. We combine maximum-likelihood (ML) amplitude estimation with a least-squares (LS) phase estimation approach known from literature to estimate the fading channel based on blocks of pilot symbols periodically inserted into the transmit symbol sequence. Furthermore, we apply Wiener filtering for interpolation of the channel estimates at the data blocks. The estimation performance of the proposed algorithms is evaluated numerically in terms of the mean squared error (MSE) and the suitability of the approach is demonstrated by evaluating the coded block error rate (BLER) for an exemplary system in comparison to the case with perfect channel knowledge. Our results show that almost the same BLER can be achieved by utilizing the derived estimation approach as compared to a system with perfect channel knowledge.