This study carried out a community survey across the 340 or so neighborhoods of the city of Chicago. Among the validated scales included in the survey are those that measure social cohesion and social capital. Respondents were asked to provide answers on a Likert scale, ranging from strongly agree to strongly disagree. A good description of the development and validation of these scales can be found in the project's publications, e.g., Sampson et al. At the neighborhood level, the social cohesion scale was found to predict variations in violent crime.
Work is currently underway to test the associations with health outcomes, such as mortality rates.
Your second question raises the issue of whether there are other approaches to measuring social capital. Unfortunately, I used my last quarter. I need to urgently get in touch with my family. As you can see, there are probably numerous creative ways to go about capturing the level of social capital in a community. The only reason they haven't been used is probably because the field is new and researchers haven't been funded to collect such data.