The urine pregnancy test (home pregnancy test or HPT) checks for the presence of the pregnancy hormone hCG in the urine. hCG is made by the implanting blastocyst and first appears in the maternal blood around implantation, on average 9 days (range: 6-12 days) after ovulation. Blood hCG levels then rise rapidly to reach a peak at 7-10 weeks. They decline after that time.
With most current pregnancy test kits (sensitivity 25 mIU/ml), hCG can be detected in the urine as early as 3-4 days after implantation, though it often takes longer. If you are pregnant, on the day you miss your period about 74% of HPTs will be positive. So a negative pregnancy test is normal in about 26% of all pregnancies, and you may have to retest until you know the results.
A negative HPT result 10+ days after the missed period makes a pregnancy unlikely. With the present generation of test kits, false-positive results due to interfering materials are extremely unlikely. Pregnancy tests have now reached a level of sensitivity and specificity that is unlikely to be surpassed either by better tests or alternative technology.