A microstate is a country with a very small physical and/or population size, yet for all intents and purposes is still legitimate and sovereign. The smallest microstates include:

Vatican City: 0.2 square miles; 350 people with Vatican citizenship
Monaco: 0.7 square miles; 32,000 people
Nauru: 8.5 square miles; 13,000 people
Tuvalu: 9 square miles; 12,000 people
San Marino: 24 square miles; 29,000 people
Liechtenstein : 62 square miles; 34,000 people
Marshall Islands: 70 square miles; 58,000 people
Saint Kitts and Nevis: 104 square miles; 39,000 people
Seychelles: 107 square miles; 81,000 people
Maldives: 115 square miles; 340,000 people

Microstates may not appear as economically viable, as a smaller population base would be required to fund its own federal government, military and infrastructure, create its own set of laws and would be the workforce servicing a tiny domestic market. Politically microstates are vulnerable to their larger neighbours (Singapore with Malaysia, Kuwait with pre-2003 Iraq). Many former colonies like Goa, Timor Leste and Hong Kong were absorbed, while the population in other colonies like Gibaltar fear absorbion if they were made independent or traded off (to the mother country, it is far safer and lucrative to stay on good terms with major powers like China and India than prop up expensive colonial pretentions).

It is therefore interesting to note that successful microstates are often:

countries with strong colonial ties to a major power that they have peacefully and progressively become independent from (often with considerable subsidies). Examples are Malta, and French Guyana.

islands, since the fixed costs of infrastructure would be equally high if dependent or otherwise. Island states are also less likely to be populated with the same ethnic group as in neighbouring countries, whose nationalists might feel they have sovereign claims to. Examples are Iceland, Mauritius and Kiribati.

countries with regal or ecclesiastical elements in their government. This helps cement the historical legitimacy of the country. Examples are Brunei, Andorra and Qatar.

(Statistics, Statistical Mechanics):

A microstate is another of those convenient fictions physicists use to give their work some degree of mathematical rigor. In statistical mechanics a microstate is a particular configuration of the particles in a system. One of the postulates of quantum mechanics is that everything we can know about a system is summed up in the system's wavefunction, so microstates in quantum mechanics are just individual wavefunctions. In classical mechanics, a microstate is just a listing of the position and velocity of every point-like particle within the system. [SM 3]

So, depending on your tolerance for super-empirical notions, microstates aren't "real" things. I mean, sure, every system has to be in a particular microstate at a particular time, but no one is going to actually observe that. For most systems, there's the practical problem of being unable to store the data — even a mole's worth of material would require much more than 10^23 bits of data — i.e., not happening in this universe, buddy.

So why talk about microstates at all? Because the things that we can observe — pressure, temperature, and so on — are macrostates linked in a one-to-many coorespondence with several microstates. And if we assume that all microstates within a closed system are equally likely (a rather contentious issue called the ergodic hypothesis) we can begin to make statistical claims about which macrostates are more likely than others. Thanks to the Central Limit Theorem and the rather large number of molecules (6x10^23 per mole) in the typical thermodynamic system, these statistical claims tend to have low variance.

In other words, if you can't see them, invent them.

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[SM] Franz Schwabl, Statistical Mechanics 2nd ed., Springer-Verlag 2002.