Normally, heritability estimates range from 0 to 1 (or 0% to 100%). A h2>1 may result from: 

i) Errors in measurement and estimation of the variances in the mixed models

ii) Relationships between parents (inbreeding)

Dear Ene Chike Onuora Theoretically, heritablity (either broad sense or narrow sense) cannot be more than unity. However, if it exceeds the upper limit, it implies negative environmental variance, which may arise due to several components of experimental error. There are instances when compoents of genetic variances turn out to be negative. However, in all such cases negative estimates are considered to be zero. You may also have a look at the previous discussion on the same topic:

https://www.researchgate.net/post/What_does_it_mean_when_heritability_is_larger_than_1

Best wishes, AKC

If it is near to then you can be considered as 99.99.

Dear Ene Chike Onuora the heritability reflects the portion of additive variance (narrow heritability) or the portion of additive and dominance variance (broad heritability) from phonotypic variance. Therefore, it cannot be more than 100 % because additive variance or additive variance + dominance variance can never exceed phenotypic variance. It is even impossible to a heritability which 100 % because of the presence of environmental variance. All the quantitative traits are characterized by the presence of environmental variance. This can be easily seen in heritability formulas:

VP=VA+VD+ VE; hN = VA/VP= VA/(VA+VD+ VE) ; hB= (VA+VD)/VP =(VA+VD)/(VA+VD+ VE)

Dear All

Thank you so much for your response.

Thank you Arbind K. Choudhary for the link you shared. I am grateful.