An accurate determination of the attenuation and phase constants (α and β) is central to leaky-wave antenna (LWA) design. While past work has relied on specialized analytical methods tailored to specific structures, this work explores numerical techniques compatible with general-purpose full-wave solvers to extract the complex wavenumber β - jα of the leaky wave on the LWA, and explores the pros and cons. For periodic LWAs, the techniques involve simulating a multicell structure and then sampling the field in each cell or calculating the S parameters at the input and output wave ports of the multicell LWA, depending on the technique used. The numerical techniques can also be used for a uniform LWA by sampling along the structure with an arbitrary sampling period.