There are several questionnaires that measure empathy or related constructs, e.g., the IRI (Interpersonal Reactivity Index; http://fetzer.org/sites/default/files/images/stories/pdf/selfmeasures/EMPATHY-InterpersonalReactivityIndex.pdf), which is quite popular and also preferable than some older measures that have unsatisfactory test criteria (e.g., Empathy Scale by Hogan), but has also been criticised to partly measure other constructs rather than empathy (see, e.g., https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2775495/). In the last paper, you also find another interesting scale, the Toronto Empathy Questionnaire (TEQ). The Questionnaire of Cognitive and Affective Empathy (QCAE) might also be of interest (https://www.ncbi.nlm.nih.gov/pubmed/21184334).
Besides questionnaires, you may also use specific tasks that present, e.g., socioemotional stimuli/scenes to participants and measures their responses. These measures test more directly empathetic processes in participants compared to self-report measures (although they also proofed useful in many contexts) and have also some ecological validity. Examples here are, e.g., the Multi-faceted Empathy Task (MET), which measures both affective and cognitive empathy components (Dziobek et al., 2008, https://link.springer.com/article/10.1007%2Fs10803-007-0486-x), the Socio-Affective Video Task, developed by Klimecki et al, 2013 (https://www.ncbi.nlm.nih.gov/pubmed/22661409); a naturalistic task developed by Rosenblau et al., (2015) which focuses a bit more on mentalizing (https://www.ncbi.nlm.nih.gov/pubmed/25267068), or EmpaToM, a paradigm that has been developed for fMRI by Kanske et al., 2015 (https://www.ncbi.nlm.nih.gov/pubmed/26254589), which measures both empathic and mentalizing (Theory of Mind) abilities. In addition, there are also tasks that measure specific abilities that contribute to empathy, but only cover aspects of it, e.g., emotion recognition abilities (see, e.g., https://www.ncbi.nlm.nih.gov/pubmed/17566449).
Stefan Schulreich gives a really complete list of questionnaires.
There is also another scale in twenty items that I currently use: the Basic Empathy Scale (Joliffe and Farrington, 2006). In this version, you assess two components of empathy: affective empathy and cognitive empathy.
More recently, other authors (Carré, Stefaniak, D'ambrosio, Bensalah and Besche-Richard, 2013) modified the classical version of BES to measure three components (BES-A): the emotional contagion; the cognitive empathy; and the emotional disconnection. In this article, you will find the questionnaire in the appendix.
see https://en.wikipedia.org/wiki/Theory_of_Basic_Human_Values — benevolence and universalism scales, but may be there are other instruments to measure empathy
Some years back I have expressed my views in this regards which I submit herewith for your kind information .
''It is the said line of action which will have experience & accepted the reality of life, we can certainly pass & help the feeling, pain & disturbance of other, the way for Empathy.