If I could get a ceramic capacitor at the capacitance of 10uF and within my voltage requirements, which from my initial searches I can, what problems would I experience if I were to change, if any?
Some circuits (like some linear regulators, for example), require a certain minimum ESR from the output capacitor, which could cause the circuit to oscillate when using a ceramic but not with an electrolytic.
In a precision circuit, a ceramic might not be preferred due to microphonics, but in those cases you probably wouldn't want an electrolytic either.
Otherwise, ceramics are generally preferred. They'll have lower ESR, they're not polarized, they need less voltage de-rating, and so on.
Finally, when searching SMD footprint standards, the common packages seem to be 0402, 0603, and 0805, where they increase in physical size respectively, but also power rating, which suggests to me I should use as large of a package as possible
Usually you choose the smallest package you can get away with because you want to fit as much circuit as you can in the smallest footprint.
Also, for ceramics, the larger sizes (1210 and higher) can have reliability issues because they can be cracked if the board flexes.
The ripple current in the output caps is a significant compared to the output current in a buck convertor running in current mode with a not too large output inductor In fact the peak to peak ripple current could be say 30% of the output current in this orthodox setup SO at 40 amps dc you need caps to handle almost 7 amps peak now the approx. current waveform is triangle so you are up for multiple caps in parallel Use big smd packages and remember that your control loop will change so you may get instability which mill mean changing compensation component values OR leaving the output electro in parallel with your new ceramic caps
Best Answer
100 µF is really pushing the limit for ceramic caps. If your voltages are low, as a few volts to 10 or maybe 20 volts, then paralleling multiple ceramics may be reasonable.
High capacitance ceramic caps have their own set of advantages and disadvantages. The advantages are much lower equivalent series resistance and therefore much higher ripple current capability, usefulness to higher frequencies, less heat sensitivity, much better lifetime, and in most cases better mechanical ruggedness. They have their own problems too. The capacitance can degrade significantly with voltage, and the denser (more energy storage per volume) ceramics exhibit piezo effects often called "microphonics". In just the wrong circumstance, this can lead to oscillation, but that is rare.
For switching power supply applications, ceramics are usually a better tradeoff than electrolytes unless you need too much capacitance. This is because they can take much more ripple current and heat better. The lifetime of electrolytes is severely degraded by heat, which is often a problem with power supplies.
You don't need to derate ceramics as much as electrolytes because the lifetime of ceramics is much larger, to begin with, and is much less a function of the applied voltage. The thing to watch out for with ceramics is that the dense ones are made from a material that is non-linear, which shows up as a reduced capacitance at the higher ends of the voltage range.
Added about microphonics:
Some dielectrics physically change size as a function of the applied electrical field. For many, the effect is so small that you don't notice and it can be ignored. However, some ceramics exhibit a strong enough effect that you can eventually hear the resulting vibrations. Usually, you can't hear a capacitor by itself, but since these are soldered fairly rigidly to a board, the small vibrations of the capacitor can cause the much larger board to also vibrate, especially at a resonant frequency of the board. The result can be quite audible.
Of course, the reverse works too since physical properties generally work both ways, and this one is no exception. Since applied voltage can change the dimensions of the capacitor, changing its dimensions by applying stress can change its open-circuit voltage. In effect, the capacitor acts as a microphone. It can pick up the mechanical vibrations the board is subjected to, and those can make their way into the electrical signals on the board. These types of capacitors are avoided in high sensitivity audio circuits for this reason.
For more information on the physics behind this, look up properties of barium titanate as an example. This is a common dielectric for some ceramic caps because it has desirable electrical properties, particularly fairly good energy density compared to the range of ceramics. It achieves this by the titanium atom switching between two energy state. However, the effective size of the atom differs between the two energy states, hence the size of the lattice changes, and we get physical deformation as a function of applied voltage.
Anecdote: I recently ran into this issue head-on. I designed a gizmo that connects to the DCC (Digital Command and Control) power used by model trains. DCC is a way to transmit power but also information to specific "rolling stock" on the tracks. It is a differential power signal of up to 22 V. Information is carried by flipping the polarity with specific timing. The flipping rate is roughly 5-10 kHz. To get power, devices full wave rectify this. My device wasn't trying to decode the DCC information, just get a little bit of power. I used a single diode to half wave rectify the DCC onto a 10 µF ceramic cap. The droop on this cap during the off half-cycle was only about 3 V, but that 3 Vpp was enough to make it sing. The circuit worked perfectly, but the whole board emitted a quite annoying whine. That was unacceptable in a product, so for the production version, this was changed to a 20 µF electrolytic cap. I originally went with ceramic because it was cheaper, smaller, and should have a longer life. Fortunately, this device is unlikely to be used at high temperatures, so the lifetime of the electrolytic cap should be a lot better than its worst case rating.
I see from the comments there is some discussion about why switching power supplies sometimes whine. Some of that could be due to the ceramic caps, but magnetic components like inductors can also vibrate for two reasons. First, there is force on each bit of wire in the inductor proportional to the square of the current thru it. This force is sideways to the wire, making the coil vibrate if not held in place well. Second, there is a magnetic property similar to the electrostatic piezo effect, called magnetostriction. The inductor core material can change size slightly as a function of applied magnetic field. Ferrites don't exhibit this effect very strongly, but there is always a little bit, and there can be other material in the magnetic field. I once worked on a product that used the magnetostrictive effect as a magnetic pickup. And yes, it worked very well.