What is the experimental evidence that light is an electromagnetic wave? Do we have any experimental evidence to confirm that light is an electromagnetic wave? Or is it confirmed simply by Maxwell's equations showing a similarity in speed?
 A: A very simple Wikipedia search gives you a lot of answers:
Electromagnetic theory as explanation for all types of visible light and all EM radiation:
Light polarisation rotates in a magnetic field (Faraday rotation), i.e. light is connected and reacts to magnetism. Maxwell's argument is of course no experimental proof, it's a theory, but all its predictions match the properties of light very well. Maxwell knew of Faraday rotation and his prediction of electromagnetic waves saw the speed close to the speed of light, so he just conjectured that they should be the same. 
Today, there are many more things that explicitly tell you light must be electromagnetic: Absorption and Emission of electromagnetic radiation can only be explained by quantum electrodynamics and the carrier particles are photons, the quantizations of the electromagnetic field. Since we can see atoms emitting visible light (some of them), this has to be electromagnetic (see e.g. LEDs). 
A: How about the fact that you can get Thomson scattering of light from free electrons that is independent of the wave frequency. The electrons must be accelerated which implicates electromagnetic fields. This would be confirmed by experiments to detect Thomson scattering from protons which would show scattered power that is less by a factor of $(m_e/m_p)^2$ as expected from the Lorentz force.
I have to admit I am not familiar with any published studies but it sounds easy enough, so should have been done.
Also the dependence of "skin depth" and the transmissivity of thin metal foils being dependent on electrical conductivity seems to implicate electromagnetic fields fairly directly. So too does the absorption of radio-waves or microwaves resulting in an alternating EMF in a conductor.
The wave nature of light is evident from any experiment involving diffraction or interference.
A: Young's double slit experiment is an excellent example of how light can be shown to be a wave.
The experiment involves firing a single beam of light at two slits, this effectively creates two beams of light which spread outwards due to diffraction (another wave property).  These two diffracting beams cross each other and cause interference where the different peaks and troughs in the waves neutralise each other.  When the light hits a surface, this can be seen as a dashed line.  I encourage you to look into it, and is an experiment you can perform at home using a laser pointer and a hair.
http://en.wikipedia.org/wiki/Double-slit_experiment
A: The fact that Marconi's machine worked!  It relies on the electric field component to affect the electrons in a long wire whuch today we call the antenna.
On an optical scale we have modern devices: nonlinear materials in optic fibers, wakefield particle accelerators, and metamaterials bending light as-designed.
The E-field and the B-field are very real, and act like any other electric and magnetic fields on the expected scale.  In short, it's been directly observed as Maxwell's equations imply would happen.
A: There is a very good article about how Maxwell's ideas (which included the idea that light was an electromagnetic wave which he actually took over from Faraday who seemed to have conjectured it first) were experimentally verified:
https://spectrum.ieee.org/tech-history/dawn-of-electronics/the-long-road-to-maxwells-equations
It was actually Heaviside who had put Maxwell's equations into its final shape and it was Heinrich Hertz who provided the first thorough experimental evidence:

Hertz used sparks in such loops [of wire of a capacitor] to detect unseen radio-frequency waves. He went on to conduct experiments to verify that electromagnetic waves exhibit lightlike behaviors of reflection, refraction, diffraction, and polarization. He performed a host of experiments both in free space and along wires. He molded a meter-long prism made of asphalt that was transparent to radio waves and used it to observe relatively large-scale examples of reflection and refraction. He launched radio waves toward a grid of parallel wires and showed that they would reflect or pass through the grid depending on the grid’s orientation. This demonstrated that electromagnetic waves were transverse: They oscillate, just as light does, in a direction perpendicular to the direction of their propagation. Hertz also reflected radio waves off a large sheet of zinc, measuring the distance between canceled-out nulls in the resulting standing waves in order to determine their wavelengths.
With this data—along with the frequency of the radiation, which he calculated by measuring the capacitance and inductance of his circuitlike transmitting antenna—Hertz was able to calculate the speed of his invisible waves, which was quite close to that known for visible light.


Heinrich Hertz used the coil (left) and the antennas (right) to produce and detect electromagnetic radiation outside the visible range.

Maxwell had postulated that light was an electromagnetic wave. Hertz showed that there was likely an entire universe of invisible electromagnetic waves that behave just as visible light does and that move through space at the same speed. This revelation was enough, by inference, for many to accept that light itself is an electromagnetic wave.

Observe that the revelation was interpreted by inference. So by showing that electromagnetic waves behave just like light in every measurable way, one concludes that light is an electromagnetic wave.
Another idea I had how to show that light is an electromagnetic wave would be to use a stronger (and well cooled) antenna (a stick in which electrons can be accelerated) than Hertz. The electromagnetic waves in the antenna have the frequency in which the electrons move up and down inside. So if one would increase the frequency more and more (by applying strong alternating voltage with ever increasing frequency), one should eventually see these radiations in form of light (as manifestation of the osciallations of electrons which are electromagnetic waves).
