Tidal channels with narrow constrictions are attractive sites for electricity generation due to energy dense, high velocity flow through the constricted zones. This work uses a 1D model to systematically examine the effect of constriction on channel potential (theoretical maximum power) and transport in channels connecting two large water bodies (Type I) and channels connecting a large water body to an embayment/lagoon (Type II). Type I channels showed a monotonic decrease in potential and transport with increasing constriction due to enhanced bottom drag from the resultant high velocity zone. The effect of constriction on potential and transport in Type II channels varies depending on the relative geometries of the channel and embayment. Type II channels may be geometrically modified to increase power and in some instances this would simultaneously produce a high velocity zone. The flow reduction required to achieve a channel’s potential was invariant to changes in constriction for Type I channels and also Type II channels if a “lagoon geometry factor” is less than about 4. A simple approximation for potential provided in the literature for unconstricted channels is extended for use with constricted channels and an approximation for the drag coefficient required to achieve potential is provided.