Methods are provided for making a porous filter that is useful in polymer melt spinning. The methods include pressing particles, such as a metal powder, to form a filter having a filter body integrally formed with a top cap and a bottom cap. The filter body and caps are formed as a single component or, alternatively, are formed as two or three separate parts that are fitted and pressed together to form a single component having blind inlet and outlet cavities. After pressing, the component is sintered to form the porous filter. The particles are pressed and cohere to form the caps and filter body without the use of a polymeric binder, and the inlet and outlet cavities are formed substantially without machining.