I was making a test render of one of my models that I've made to look good in Eevee with Screen Space Reflections and Contact Shadows, but I saw that both of them clip near the edges of the camera. I know screen space effects only apply to objects visible, but is there a way to fix this clipping without having to completely ditch the screen space effects or resort to Cycles?
Screen Space effects such as Shadows are a technique (borrowed from game rendering) to improve the visual look of a render without having to spend too much additional time considering features that are not visible. As such, it is a trade-off between realism and fast renders. Only 'visible' components are considered and so there can be noticeable issues with elements towards the edges of the visible frame.
One way to resolve this is to render an additional border around your frame by increasing the camera Sensor Size. This will have the effect of rendering additional area around the frame without affecting the perspective of the camera. The additional space will be used for rendering screen space reflections, etc. and you can then use the Compositor to clip the unwanted section from the final render.