Hello, Ilan! Since so many efforts to gain soft power are carried out through public diplomacy initiatives, one good measure of the soft power achieved would be the results obtained by such initiatives. For instance, the cultural diplomacy outcomes for a country could be grasped in terms of how many people has come to view its films, listen to its music and access its websites, and so on. Educational and scientific diplomacy outcomes, by their turn, could be seen in the increase in foreign students, international cooperation partnerships, or citation of publications from national authors (as can be evidenced by Bibliometrics). How these somewhat immediate impacts are going to affect policies and politics, however, would require a more longitudinal approach. It would require, for example, to see how many of these exchange students have risen to leading positions as scholars, strategists and politicians in their countries of origin and to observe their interpretations concerning the foreign countries in which they studied. As soft power and hard power are frequently intertwined, economic flows (FDI, trade, stocks) can also be analyzed before and after international promotion events (from fairs to seminars to diplomatic missions) organized by governments. The opening of consular offices can likewise represent the growth of the interest in a country’s affairs overseas. Finally, a more superficial (yet equally easier) approach would be to review what has been said of a country in foreign media. Some examples of studies undertaken aiming to assess soft power and public diplomacy efforts can be found in the web. Two important remarks: (i) you may notice I have only referred to countries in these lines. Nonetheless, other kinds of players (nationally-bound and international organizations, movements and individuals) may as well develop and employ their soft powers; (ii) people assessing others' soft power also have their own agendas, so always be mindful of the possible biases in this kind of analyses. Best regards.

http://www.instituteforgovernment.org.uk/sites/default/files/publications/The%20new%20persuaders_0.pdf

You may also find interesting this Public Diplomacy monitor by the University of Southern California.

http://uscpublicdiplomacy.org/index.php/pdin_monitor/

You should look at the IfG-Monocle Soft Power Index and the Soft Presence indicators of the Elcano Global Presence Index

check out my research on measuring and mapping soft power of institutional actors, such as museums https://pursuit.unimelb.edu.au/articles/putting-museum-power-on-the-map

and my academic article on this is here: Article Mapping museum 'Soft Power': Adding geo-visualization to the...

Soft Power 30, a Portland based independent think tank is also good source to look.

https://softpower30.com/

In my Ph.D. research, I study soft power deployed in the government's propaganda system, so I use the approach of Bernett and Duvall (2005)'s model to analyze both of soft power and propaganda in Chinese context.