What are the technical solutions to measure $\ce{CO2}$ emissions? I'm currently at COP24 (United Nations Climate Change Conference) in Katowice, Poland.

(some editing since I took a screenshot of my laptop)
I've asked some guys about $\ce{CO2}$ emissions but very few have sufficient technical knowledge.
My assumption is that they assume the data is right.

Some Google-fu:
https://ourworldindata.org/co2-and-other-greenhouse-gas-emissions#how-do-we-measure-or-estimate-co2-emissions

More recent energy statistics are sourced from the UN Statistical Office, which compiles data from official national statistical publications and annual questionnaires.

https://www.thenakedscientists.com/articles/questions/how-do-you-measure-carbon-dioxide-emissions

The Intergovernmental Panel on Climate Change has published a five-volume set of guidelines that all the countries now use, as part of the UN Framework Convention on climate change, for estimating emissions on all greenhouse gases and it does produce uniformity across countries.
Although there are some large power plants in which they actually put measurement devices in the smoke stack and can measure the amount of CO2 that comes out, that is unusual.


About measuring $\ce{CO2}$ in the atmosphere, we have a satellite for that: https://climate.nasa.gov/climate_resources/99/graphic-measuring-carbon-dioxide-from-space/
About air quality index - https://en.wikipedia.org/wiki/Air_quality_index - we have a number of standards for that (shame there are multiple standards)
About new $\ce{CO2}$ emissions - what are the scientific ways to measure that?
In addition to satellite measurements of carbon dioxide, there are numerous ground based stations that also measure carbon dioxide: Italy, Hawaii, Australia, just to name a few.

If you want to catch carbon dioxide emitting cheaters, a dense network of such ground based stations would be needed around the world. The measurements would need to combined with meteorological data, particularly wind directions and strength. I imagine this would also require significant computer modelling to analyze all this data in a timely manner. This would need to be operated by a totally independent organization with lots of money. This will be difficult to achieve.

Alternatively, and probably more costly would be to have a constellation of satellites in geostationary orbit around the Earth constantly measuring atmospheric concentrations of carbon dioxide. As with the ground based stations, the data would need to be combined with meteorological data and processed via a computer model.

Monitoring compliance will not be cheap or easy.