For less social species, such as some finches or canaries, they are more independent and they do not require constant companionship. Providing them with a comfortable living environment and meeting their basic needs, including food, water, shelter and access to a healthy diet, may suffice.
Consider consulting with an avian veterinarian, a bird behaviorist, or a local bird rescue organization for species-specific advice and support to ensure the well-being of the bird while grieving and adapting to the loss of its partner.