I don't think there is an "homology score". Homology is defined in terms of shared ancestry, usually inferred by similarity - for which you can have a score. You may have partial homology, if a gene arose by fusion of two ancestral genes, even so I don't think "homology scores" are used.

Regarding your question, you can use blast to search for paralogs (homologous genes which arose by duplication inside one genome). Indeed, blast has been used many times do to exactly what you want.