It's a good idea to get information from different informants. In my lab, we have used a number of different measures, but the ones detailed above are useful and well documented in the literature. We have also used Susan Harter's perceived competence scale, which has always given us good reliability. The SDQ is a standard measure used by school and clinical psychologists in the UK and it has proved to be of benefit when assessing certain groups. Hope that info is useful.
I would recommend the Harter Self Perception Profile surveys, by Susan Harter. They measure different dimensions of the self-concept related to perceived competence and self-importance (including the social domain). There are separate questionnaires for children, adolescents, college students, adults, older adults, and individuals with learning disabilities, with slightly different dimensions, based on relevance to a given age group. You could use these to look at social competence alone, or social competence compared to competence within other domains. You can also compare self-report with parent or teacher ratings.
These questionnaires are posted online for free. https://portfolio.du.edu/SusanHarter/page/44210
I use a combination of tools including a home "grown" one. I like the Conners as it has an early childhood component as well as a tool for children seven and above. But as it has been mentioned prior to my joining the conversation, the usefulness of rating scales is limited to what you are measuring. I like conducting interviews and asking questions about social competencies in different settings such as home, school, church and after school programs such as Boys Scouts/Girl Scouts, Boys and Girls Club or daycare. You can get a very skewed picture of a child by looking at only one or two settings thus I use a locally developed interview of social history as well as a functional behavior assessment questionnaire which also identifies the lagging social skills of children. You might try looking up the ALSUP. None of these tools are stand alone measures but in conjunction together they can shine light on social strengths and weaknesses. Another person who has researched in the area of social competencies is Brad Chapin in the realm of self-regulation. He has some VERY USEFUL tools that I use with parents looking for some on the spot helps that work.