The above example using sort is close, but in the case of strings simply use SearchString:
files := []string{"Test.conf", "util.go", "Makefile", "misc.go", "main.go"}
target := "Makefile"
sort.Strings(files)
i := sort.SearchStrings(files, target)
if i < len(files) && files[i] == target {
fmt.Printf("found \"%s\" at files[%d]\n", files[i], i)
}