Check on is an essential word that we frequently use in our daily conversations. However, if you're looking for synonyms that mean the same thing, then there are a few options you can try. For instance, you can use the word 'verify' to mean checking on someone or something. Another synonym that would work is 'monitor' - to keep an eye on someone or something. Additionally, 'inspect' can be used if you want to look over something carefully or to investigate a particular item or person. Other synonyms that are synonymous with the phrase "check on" include assess, review, scrutinize, and analyze. Overall, these alternatives will help you get your point across and achieve the same result as using the original phrase.