According to Memory Alpha the supernova was a nearby star, (but supposedly NOT the star Romulus and Remus orbited). This is never clearly explained or diagrammed so we can understand how this happened. (For this example we will assume it was the Romulan star which went nova to explain potential effects.)
In 2387, a star close to Romulus went supernova, endangering the entire galaxy. Ambassador Spock created a red matter singularity which consumed the star, but not before the supernova reached Romulus, destroying the planet. (Star Trek)
Romulus (and presumably Remus) is destroyed in the supernova.
Given the explosion was clearly seen to engulf Romulus in a fiery wake, the star had to be relatively close, otherwise, the Romulans would have (and should have) been able to evacuate in a timely fashion.
Normally, any planets within the orbit of a star going supernova are more than likely destroyed in the resulting blast. Remus was the third planet in the Romulan star system so it was likely as destroyed as Romulus was.
In a normal supernova, the energy of the explosion is strong enough to strip away even the dense atmospheres of local gas giants, leaving only their metallic or compressed matter cores. Depending on the size of the star and the distance between the local stars, nearby star systems can be affected by gamma ray and other radiation effects.
During this short interval of a star explosion, a supernova can radiate as much energy as the Sun is expected to emit over its entire life span. The explosion expels much or all of a star's material at a velocity of up to 30,000 km/s (10% of the speed of light), driving a shock wave into the surrounding interstellar medium. This shock wave sweeps up an expanding shell of gas and dust called a supernova remnant.
All supernova are not created equal but most will have devastating effects on their local star systems. This can include emissions of gamma ray pulses and other energetic radiations including dangerous cosmic rays. In extreme conditions, the star's collapse could even result in a singularity or black hole.