The proliferation of printed electronic devices is feeding the growth of the Internet of Things, with devices deployed everywhere to collect and communicate data. At the same time, the increase in low-cost disposable devices is a cause for serious environmental concern. In particular, widely used plastic substrates such as poly(ethylene terephthalate) are persistent hazards to the environment. Paper is promising as a greener substrate for printed electronics because it is biodegradable and sourced from renewable materials as well as being low cost and compatible with roll-to-roll printing. However, the porous microstructure of paper promotes wicking of functional inks, leading to poor electrical performance and printing resolution. Hydrophobic coatings applied to the surface of paper create a planarized, printable surface, but these materials may compromise biodegradability and/or recyclability. This paper describes a new resist-free patterning method for printed paper-based electronics that takes advantage of the porous structure of paper. Debossed contact printing uses the pressure from a debossing tip to compress the porous structure of paper and create a patterned relief structure. Printing functional inks with an unpatterned roller deposits ink only on the raised regions of the relief structure. We demonstrate debossed contact printing of silver, carbon black, and conducting polymer inks and show that this new fabrication method is suitable for the fabrication of printed devices with dense features. We demonstrate the fabrication of antennas and patterned electrodes for RFID and smart wallpaper applications, respectively.