From my individual perspective, emotional intelligence itself can only be measured as an ability. Not everyone thinks this way, of course, and other scales are available. Even if you agree with me, the MSCEIT may not be a good choice in every instance. The test may take too long, or otherwise be inappropriate for use with a given sample.
One possibility is to examine a particular ability area of EI in greater depth: That is, experimental studies can be conducted on the processes behind making emotionally-intelligent judgments or perceptions. Some research related to EI can be found in two books: The Wisdom of Feelings (Barrett & Salovey) and Emotional Intelligence in Everyday Life (Ciarrochi, Forgas, & Mayer). An often broader collection of research can be found in the Handbook of Emotions (Lewis and Haviland-Jones) and the Handbook of Emotional Intelligence (Bar-On & Parker).
In addition, many self-judgment tests of emotion-related phenomena may provide a reasonable alternative that is different, and (mostly) uncorrelated with emotional intelligence, but could provide important contributions to the emotions area (If you are interested in personality traits more generally, see www.thepersonalitysystem.org).
There is, for example, the option of simply measuring a person's mood at one time, or several times, and correlating the mood with a critrion. The Brief Mood Introspection Scale (BMIS) can be downloaded from this site for that purpose (see the Measuring Mood, Meta-Mood, and Empathy section).
My colleagues and I have developed a number of scales of the meta-experience of mood and emotion. These self-report measures assess dimensions such as how clearly a person believes he or she can perceive ongoing mood states, and how acceptable the mood feels for the individual. Both state and trait measures of such reflective experiences are available.
The "State Meta-Mood Scale" is published in an appendix to this article, which can be downloaded (see also the "Reprints on Cognition and Affect" section). The scale is quick and interesting to use, and has a number of interesting correlations with other measures.
The "Trait Meta-Mood Scale" is also a published scale which can be downloaded from here and employed. That scale, too, is quick and interesting to use, and has a number of interesting correlations with other measures.
There is a broader area of mood regulation, for which many scales have been written and are increasingly used. These scales ask people everything from how much they think they can change their moods, to how frequently they try to do so. Check the research of James J. Gross, Barbara L. Frederickson, or W. Gerrod Parrott as starting points.
Another possibility is to use the Mehrabian-Epstein empathy scale, or the Davis Empathy scales.