When we have proved that Tawaf on behalf of Imam (aj) is Mustahab (recommended) then it is understood that sending someone in lieu of Imam (aj) would also be Mustahab. Because this is a result of friendship and gratefulness. Therefore its merit and goodness is proved by reason. To send a person for Hajj as a proxy on behalf of Imam (aj) is naturally more rewarding than sending a person to perform a Tawaf.
However, there are some particular actions that are specially recommended (Mustahab) on behalf of the Living Imam (as). The same are mentioned in the book of Al-Kafi in a tradition of Imam Taqi (as) reported by Musa bin al-Qasim. The narrator says that he asked Imam (aj), “I wanted to perform Tawaf on behalf of you and your forefathers (as) but people said that Tawaf was not permitted on behalf of the successors (awsiya)?”
Imam (aj), “Rather, you must do as many tawafs as possible.” The narrator says that after a period of three years, again he came to Imam (aj) and said, “I had previously obtained permission from you to perform Tawaf on behalf of you and your father. After this I performed as many tawafs as Allah willed for me on behalf of you and your respected father. After this I had an idea!” “What was it?” asked Imam (as). “One day I performed Tawaf on behalf of the Messenger of Allah (S).” Imam (as) recited Salawat on the Holy Prophet (S) thrice. The narrator continued, “On the second day I performed Tawaf in lieu of Amirul Momineen (as), then for Imam Hasan al-Mujtaba (as), Imam Husain (as), Imam Sajjad (as), Imam Baqir (as), Imam Sadiq (as), on the eight day I performed it on behalf of your grandfather Imam Musa al-Kazim (as). On the ninth day for your respected father Imam Reza (as) and on the tenth day I had the fortune of performing Tawaf for your respected self. (as). I worship Allah through the Wilayat of these personalities.” Imam (as) said, “By Allah! You are worshipping Allah through a religion (din) other than which Allah will not except any din.” The narrator said, “Often I have performed Tawaf on behalf of your respected grandmother, Fatima Zahra (s.a.) and sometimes I didn’t.” Imam (as) said, “Do more Tawaf! If Allah wills it will be the best action performed by you.”1
Among the things that prove that it is recommended to do Tawaf on behalf of general believers is a tradition that is mentioned in Kafi through the author’s own chain of narrators from Abu Baseer from His Eminence, Imam Ja’far Sadiq (as) that he said: One who does a good turn to the father or a relative and performs Tawaf on behalf of them, will get the full reward for it and one for whom he has performed the proxy will also get the same reward. And since the person has accorded importance to the relationship of that person, in addition to the reward of the Tawaf he will get extra rewards.2