Unfortunately the number 1 thing most employers look for is work experience. Since you talk about certification and home system it makes it sound as if you don't have much work experience.
You might ask the people who were offering the certification classes as they may have contacts.
Also you don't say WHERE you are. If you're in a fairly large city there may be a local UNIX user's group or at least a Linux User's group. Going to meetings for one of those might help you find some leads or least make contacts of your own. If you're in the U.S. posting on Monster.com will likely get you more hits than anything else.
Recruiters typically do keyword matching so you might want to think of a technologies resume if your work experience is light. e.g. List OpenSolaris (and Solaris by itself - some recruiters might not realize its the same thing). Also list hardware, applications, databases you may have been exposed to. (Note: Don't lie on the resume but do list things that are on OSes you've supported even if you're not an expert in the app or the database - some employers are looking for people who have supported similar environments.)
Also you might want to look into "Operator" positions especially for afternoon/night shifts which are harder to fill. While not true "Administrators" sometimes starting in such a position can put you in place for a true "Junior Admin" position down the road.