For the House, the average population of a district would be 667,761 which is close to the US, I think- so that works well. Also, Malta- the smallest country is not that much smaller than Wyoming.
For the Senate, you could do 2 for each country, for 52 Senators but that would be rather small, and then you would have Germany and Malta with the same about of Senators which is worse than the US.
Alternatively, you could give each NUTS region 2 Senators, for a total of 194 Senators. Only problem here is you get countries like the Czech Republic with only 2 Senators, when other countries of similar sizes would have more (like Belgium).
I think 2 for each countries is the most sensible, even though the difference between Germany and Malty of course is very big. As far as I understand it the purpose of the senate and equivalent organs is to represent the "cultures" (for lack of a better word) rather than the individuals so that the smaller ones does not disappear by being overwhelmed by the bigger ones.
I guess such a system would increase the trend towards regions wanting to become independent (Scotland, Catalonia etc.).