It is believed that Lord Shiva is the first and the most ardent devotee of Lord Rama.
In the Padma Puranam (within the Vishnu Sahasranama phalasruti), Lord Shiva tells Goddess Parvati that he constantly meditates on and delights in chanting the name of Rama ("Sri Rama Rama Rameti Rame Raame Manorame, Sahasranamathatthulyam Raama Naama Varaanane"), declaring that chanting it three times equals the merit of the entire Vishnu Sahasranamam.
This devotion is also said to be one of the main reasons why Lord Hanuman, being one of Lord Shiva’s amshavataras. The Shiva Purana explicitly states that Lord Shiva took an incarnation or a form as a vaanara—Lord Hanuman—to assist Lord Vishnu in his avatar as Lord Rama. Lord Hanuman is often regarded as an eleventh Rudra (an aspect or manifestation of Shiva). And the relationship shared by Lord Rama and Lord Hanuman needs no preamble!
Jai Shree Ram! Om Namah Shivaya!