A theoretical model for forbidden ortho-para absorption in molecules having weak intramolecular mixing of spin isomers is developed. The model is based on the quantum kinetic equation for the density matrix and uses the particular case of CH313F nuclear-spin isomers for numerical calculations. Forbidden ortho-para absorption appears to be very small, making its detection difficult in a standard approach. Two alternative methods for detection of forbidden ortho-para absorption are proposed. The methods use microwave enrichment of spin isomers and microwave speed up of the isomer conversion.