Your question is too broad to answer it with a simple message. Theory of mind seems to be related to mental models or a way you perceive the objects/people in the world and yourself too. It is a THEORY. So it is related to emotions and social cognition, since emotions, for example, are a part of this theory. Emotion is different from emotion perception. Either you talk about perception of others' people emotions, or about emotions experience by the participant. Please specify what you are interested in.
Social cognition is aboutcognitive processes in social environment/intractions.
As you are too unspecific, it is hard to recommend a task. Emotions can be manipulated or measured (SAM for self-reported measures, Bradley & Lang, 1994; PANAS, too. Physiological factors as direct measurements, or fMRI too). For social cognition there might be questionnaires. You can also try causal mapping (Markoczy & Goldberg, 1995).
Hi Amir, looking at your questions and the research you are undertaking to explore high social cognition, it might be worth considering a main focus to be social cognitive functioning as the prime research question and that can subsume theory of mind. The way emotions and feelings are construed is really emotional perception, self and other.
Daniel Goleman has written a couple of books, Emotional Intelligence and Working with Emotional Intelligence where he identifies 5 main areas that constitute emotional intelligence.
Recognise your emotions, manage your emptions, stay motivated, recognise emotion in others' and handle relationships. There is some discussion about whether emotion intelligence exists or if it is really part of personality. That said, the idea of recognising emotion in others, staying motivated and handling relationships fits in with your second order perspective and social cognition. You might use a scale to measure second order principles in your research. Goleman continues to spread his word on EQ so you could check him out on the net. Also, It may be useful for you to check out the sociality corollary proposed by the personality theorist George A. Kelly in the Psychology of Personal Constructs.