Planar leaky-wave antenna (LWA) designs that utilize a printed surface wave (SW) source are presented. Specifically, by the addition of a periodic arrangement of width-modulated microstrip lines on top of a grounded dielectric slab (GDS), a sinusoidally modulated reactance surface (SMRS) can be realized, providing appropriate conditions for leaky wave (LW) radiation. In addition, a transition section near the SW source improves antenna matching, while also, controlling the leakage rate and aperture distribution. A numerically computed dispersion diagram (DD) for the periodic structure is also calculated in terms of Mathieu functions. Full-wave simulations and measurements are in agreement with the developed numerical model and results suggest that these LWAs can offer broadside radiation as well as continuous beam scanning with radiation efficiencies of more than 85%. In addition, the investigated width-modulated microstrip lines offer ease of fabrication and may also be useful in the design of new periodic structures for wave guidance and other low-cost printed circuits and antennas.