If someone would have obtained two MSc degrees from the same university for example MSc politics from UCL and MSc international relations from UCL too, how do you put that on a business card?
This will very likely depend on the laws of the country you are in and the norms of the business you are in (does it look complete or pretentious to list all degrees). For example, in Austria you would/could just list all titles (except if you work in an especially "young" company where you would probably not list degrees at all).
Since you seem to emphasize "from the same university", could you mabe explain why this could make a difference to "two master titles from different universities"?
Generally, it is up to you, but it is good to follow the customs and culture of the country and the workplace.
E.g. many universities and government positions will try to list all your titles, both of the respect to you, but also to give a better representation of the person in mind.
Many companies would also want to show that they have highly-skilled workers to their customers/partners. It is interesting to note that (at least from my experience) most companies will only include one (usually the top one) title. This is mainly done not to look too pretentious, but also to make it easier for any person who would read your business card to understand your general position without having to take a minute or two understanding how all the titles line up.
Some of the answers question why you want to include all your academic qualifications on a business card. Whether or not to do so, is very much a matter of local custom and practice. Only you, seeking advice locally if you wish, can decide whether you should do so.
If you want to include them then the answer is clear: you are John Doe, MSc(Somewhere), MSc(Somewhere). Such a formulation might give rise to questions, but so what? You have a good story to tell.
You might like to check what the relevant university's exact title for your degrees is: are they both actually MSc? The exact abbreviation might differ. One of mine is in fact MMath, and another is in fact MSc, but the previous year's class got MSc(Eng).