Energy and momentum conservation laws in special relativity

In special relativity the energy of a material point is defined
$$E= frac{m_0}{sqrt{1-v^2/c^2}}c^2,$$
and the momentum is defined by
$$mathbb{p}= frac{m_0}{sqrt{1-v^2/c^2}}mathbb{v},$$
where $mathbb{v}$ is the velocity of the particle.

I am wondering whether the conservation laws of energy and momentum in special relativity have been verified experimentally. At this point I would prefer avoiding quantum effects if possible.