<p>We use three-dimensional numerical simulations based on the lattice Boltzmann method to study how an ellipsoidal microscopic swimmer moves through a square microchannel. Three key factors are varied: the strength of inertial effects in the flow, the swimmer’s shape (from spherical to three times longer than it is wide), and the degree of confinement by the channel walls (from narrow channels about three swimmer diameters across to wider channels about eight diameters). We consider both pushers (which drive the fluid backward with their rear end like sperm cells) and pullers (which pull the fluid forward with their front end like algae). As inertia increases, pushers swim faster whereas pullers slow down, and the change in speed is much stronger for pushers. The swimming speed can be captured by a simple quadratic trend when expressed in terms of a single combined measure of inertia and swimming stroke. More elongated swimmers move faster overall and are less influenced by inertia, while nearly spherical swimmers are the most sensitive to changes in inertia. As the channel becomes wider, the walls constrain the swimmer less, and variations in inertia have a more pronounced impact on the swimming speed.</p>