Moving contact lines in microchannels play a central role in many porous-media and microfluidic processes, yet they remain challenging to simulate accurately due to the stringent requirements on curvature and surface-tension evaluation near solid boundaries. We investigate contact-line dynamics in microchannels using direct numerical simulations within a volume-of-fluid (VOF) framework. To this end, we develop a height-function-based contact-angle enforcement method applicable to both flat and curved solid surfaces. The key idea is to incorporate the contact-line position into the curvature estimation in those cells containing contact lines. On flat solid walls, the proposed model achieves higher accuracy than the conventional vertical height-function method for enforcing very small and very large contact angles \cite{Afkhami}. The method also extends naturally to curved solid surfaces represented by the embedded boundary method. Building on this implementation, we study moving contact lines in microchannels with a range of geometries, including straight, sinusoidal, and multi-branch microchannels (see the sinusoidal example shown in Fig.~\ref{fig:fig1}). The relevant flows are characterized by small capillary number (Ca) and large Laplace number (La), which amplify the sensitivity of the solution to the curvature error near the contact line. We systematically analyze spurious currents—manifested as pressure and velocity oscillations within the channels (representative velocity oscillations are shown in Fig.~\ref{fig:fig2})—over wide ranges of capillary and Laplace numbers, with Ca down to $10^{-6}$ and La up to $10^{6}$. The results help clarify the mechanisms underlying the numerical contact-line pinning and other limitations of existing contact-angle enforcement strategies \cite{Tavares,Chen}. Overall, these microchannel configurations provide a demanding set of benchmarks for assessing contact-angle models on embedded solid surfaces.