One solution is to travel with groups that offer to arrange roommates.
On our Eurynome Journeys WanderWoman™ trips approximately 80% of our clients are single female travelers and only 20% of them request single (private) rooms. So we match our travelers with roommates, as do many other women's travel companies. We have found this to be very successful.
Right now (10 May 2011) we have two women-only trips with room shares available:
Maine Coast: Art & Nature Tour in July
New Years' Escape: Roman Holiday in late December
If you prefer not to travel with a group, another option is to join an online travel community and look for like minded travelers in the same predicament.
One great resource is: http://globetrooper.com/
Another site to find travel companions, geared exclusively to women, is Thelma & Louise.
And of course every female traveler should check out the resources on Journeywoman.
If you are planning to travel with someone from an online community exercise caution and read safety guidelines provided on these sites.
LIVE, LAUGH & TRAVEL!