How to extend styled component without passing props to underlying DOM element?

2020 UPDATE: Use transient props

With the release 5.1.0 you can use transient props. This way you do not need an extra wrapper i.e. unnecessary code is reduced:

Transient props are a new pattern to pass props that are explicitly consumed only by styled components and are not meant to be passed down to deeper component layers. Here's how you use them:

const Comp = styled.div`
  color: ${props => props.$fg || 'black'};
`;

render(<Comp $fg="red">I'm red!</Comp>);

Note the dollar sign ($) prefix on the prop; this marks it as transient and styled-components knows not to add it to the rendered DOM element or pass it further down the component hierarchy.

The new answer should be:

styled component:

const ResizableSC = styled(Resizable)``;
export const StyledPaneContainer = ResizableSC.extend`
    flex: 0 0 ${(props) => props.$someProp}px;
`;

parent component:

const PaneContainer = ({ children, someProp }) => (
    <StyledPaneContainer
        $someProp={someProp}  // '$' signals the transient prop        
    >
        {children}
    </StyledPaneContainer>
);

As suggested by vdanchenkov on this styled-components github issue you can destructure the props and only pass the relevant ones to Resizable

const ResizableSC = styled(({ someProp, ...rest }) => <Resizable {...rest} />)`
    flex: 0 0 ${(props) => props.someProp}px;
`;

For those (like me) that landed here because of an issue with SC and react-router's Link.

This is basically the same answer as @tskjetne, but with JS syntax style.

const StyledLink = styled(({ isCurrent, ...rest }) => <Link {...rest} />)(
  ({ isCurrent }) => ({
    borderBottomColor: isCurrent ? 'green' : 'transparent',
  }),
)