Well, I can't say that I've encountered others, but the Swiss system works very well.
Translated from german, the name of its from of government would be "semi-direct Concordance-Democracy".
Semi-direct means that the people ge to vote on (almost) everything, have the right to veto anything the govt does (Referendum) and propose new constitutional amendmends or laws (Initiative) but that we don't choose the executive branch ourselves and that we have a parliament.
This parliament is made up of two houses: The Council of States and the National Assembly. Both are elected by the people directly and does, in my opinion, reflect the views of the swiss populace quite well.
The judicial and the executive branches are not voted on directly by the people, but that makes sense in both instances. The judges are hardly known around Switzerland, so it would be nigh nonsensical to have a citizen who, most likely, has never even encountered a judge try and decide which judge is best suited for the High Court.
For the executive branch the situation is not quite the same; for one thing, EVERY swiss citizen is eligible to be elected Federal Councillor, no matter who they are, so it might well happen that everybody votes for their grandma. Then there are the questions of competence and concordance. Competence can hardly be judged by people not involved in parliamentary decisions (I found out only recently that we have MPs that focus on certain topics AND I CARE ABOUT POLITICS!) and Concordance would not be respected in a popular vote.
What does concordance mean? It means that no major party really is in opposition, they're all in the government. It means that the federal councillors aren't involved (as much) in party politics and instead work together to find compromises.
There's the so-called Magic Formula: 2 Social Democrats (Americans would call them Socialists), 2 Liberal Democrats (center-right with focus on business), 2 Swiss People's Party (nationalists; getting ever more populist and shifting right) and 1 Christian Democrat (what it says). Currently this is broken, as the SPP expelled one of their Federal Councillors who went to join a new conservative party. Still, it is expected to be restored at the next election.
Head of state is the President of the Federation; one of the Federal Councillors chosen by rotation. It is a purely representative position, so that there's someone we can present as Head of State.
If you wish to know more, Wikipedia has decent information and I could also elaborate more on some details, but I think this makes for a reasonable answer to your question.

I don't profess to know which is the best or most representative system, as my experience of those other than the UK model is limited.

Leaving very dodgy/dictatorial systems aside. The way I see it is most proposed systems are flawed and by it's nature any system will be because you must in someway filter the representation so that you eventually get a small number of people representing a larger body of people. This way not everybody will be truly represented unless everybody got to vote on everything.

Furthermore some parts of society may be less inclined/unable to vote and will thus be under represented not because of the system but because they are either not given, able to or motivated to vote.

A key part of "Representative" is to increase the sample size casting a vote, therefore giving more statistically representative results. Whether first past the post, Proportional Representation, electoral colleges (inc. super delegates) or whatever else, the basics come down to numbers voting. How those then get divided amongst the protagonists is the final part of the question.

Direct Party and Representative Voting is the system that most accurately reflects the wishes of the electorate in a party based parliamentary democracy such as the UK. This is because you have one vote for the party of your choice and one vote for the representative to represent you and the Constituency. It gives the most accurate PR result for the formation of the Government, but still lets you choose the best MP for your local constituency.

The features of DPR voting are Accurate PR Government – every vote counts No opportunity for Tactical voting No Safe Seats No Campaigning based on Marginals A vote for your party even when there is no candidate standing in the constituency. A vote both for the party you want to form the Government, and also a vote for the candidate you want to represent you and your constituency. A single MP to represent the Constituency so elections retain their local character An MP elected on merit, track record and personal qualities

It is also Very easy to understand the system Very easy to vote Very quick and simple to count Very easy to administer

It requires very little change to the current electoral system.

For more about Direct Party and Representative Voting – see www.dprvoting.org

Your title asks, "What is the most representative electoral or voting system?"

Even theoretically or mathematically, no "fair" voting system can satisfy these three criteria:

• If every voter prefers X over Y, then the group prefers X over Y.
• If every voter's preferences between X and Y remain unchanged when Z is added to the slate, then the group's preference between X and Y will also remain unchanged.
• There is no dictator.

This blows my mind. Read more about Nobel Prize (for Economics) winner Kenneth Arrow's impossiblity theorem.