Oregon death certificates cannot be publicly assessed for the first 50 years after they are published. They are restricted to family members and representatives of the immediate family. You must first contact a member of the immediate family to get written and notarized permission to access them. Once you have this, the record may be acquired from the Oregon State Registrar with the Center for Health Statistics which you can access at Oregon.gov. If the certificate is more than 50 years old, it is considered public record and is available through the state archives. The process is much easier and much less restrictive than the procedure for newer records.
The death certificate will tell you when and where the person died as well as the recorded name at the time of death. All of this is important to narrowing down the location of obituary records, and it can greatly help reduce the amount of ground that must be covered if you are not aware of the exact location or date of the death.
Unfortunately, finding the actual obituary does not get much easier from there if you don't know the publication that it was run it. The problem is that there is no comprehensive index of Oregon newspapers that allows for a search of a database. Libraries often don't have any way to index them unless they devote massive teams of their own staff to do the work. Publicly funded libraries are often understaffed to begin with, so it becomes more difficult by the day to find people to take on this undertaking.
If you know what paper the published the obituary and when it may have been completed, then it should not be difficult to hunt it down. You can follow up with the newspaper itself. Get in contact with their archives department to see if they have a procedure for locating pages in older issues. If the paper isn't published any longer or the newspaper is not able to assist with an archives search, it's time to move on to the record keeping authority in most cities-- the library.
Local libraries often keep comprehensive records of newspapers that were published in the area or that may have mention of the area. For instance, a paper published right outside of Portland might be kept in archives at a Portland-area library as well as a library in a suburb of Portland as long as it's part of the major metropolitan area.
However, cities with major universities may be in luck when it comes to finding comprehensive collections of newspapers. State universities like the University of Oregon often keep entire collections of newspapers in their archive. In this case, University of Oregon has a microfilm record of just about every newspaper that was published in Oregon. This means that if you are able to narrow down the search to a year as well as a publication, your search could be manageable.
You can manually search through to find the newspaper that you are looking for by heading to the shelves that hold all of the microfilms. From there, you will find that they are divided by city and then by the name of the paper.
While it is not complete, the University of Oregon is attempting to make the process of finding newspapers easier by providing an index of titles that have circulated in Oregon. This list enumerates every title that has been kept on microfilm at the University of Oregon library and indicates where they can be found in the microfilm collection. It's helpful because it is separated by city or county.
If you know at least the county where the person in question died, you can cross reference the year or decade with the publication dates for the paper. Often, what you will find is that there are only two or three newspapers that were active in the city at the time. Searching by county may yield more results of active papers at the time, but it's still a greatly reduced number.
If the obituary was published in the Portland-based Oregonian, you may be able to find it by without having any information other than the name of the deceased and an idea of when he or she passed away. On online index as maintained by the Eugene Public Library offers a search engine that allows users to remotely access an index to figure out what issue the obituary was published in. The index covers more than 150 years of history from the Oregonian.
Even if you aren't sure that the obituary would show up in the Oregonian, it can't hurt to take a few seconds and do the search. It might make the process a whole lot easier than you realized. The same search engine also offers access to the 40 years of archives from the Register Guard.
Oregon libraries also offer access to documentation in card catalogues that keep reference of all of the obituaries that are contained within the archives.
If the obituaries that you are looking for exist from the beginning of the 20th century, there is a resource that will allow access to images of the actual newspaper. The Historic Oregon Newspapers site has documented copies of entire papers that are available from the website for reading and perusal. The documents are also tagged and searchable, so you should be able to enter a name and get any results from any Oregon papers that have that name. These issues encompass most Oregon publications and go through 1922. Copyright limitations that make it more difficult to digitize issues that were published after that.
Though they are not contained in one place, Oregon libraries and organizations provide plenty of opportunities to find the details that you need. It requires some extra leg work, but it's not an insurmountable task.